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1. Lambda lt X gt spin independent lt X gt 1 and spin dependent lt X gt 2 interparticle in teraction strength respectively for each level Real array dimension 10 de fault 0 dO It is important to note that it is necessary to specify at least as many one body potentials as there are levels or spinor components in the treated particles a conical intersection the number of potentials is NLevel 1 In the case of atoms featuring This is done in the routine Get _NLevelPotentials in the Get_1bodyPotential F source file The available predefined mul tilevel potentials are collected in the following table whichpot Description Potential Parameters HO1D Parabolic potentials with V z SP p p2 are the frequencies of different frequencies and off V x 3p3 a ps pa _ the components levels set for different spin compo respectively p3 is the hor nents or levels This poten izontal displacement of the tial is defined for two level or two parabolas and p4 their spin atoms only relative offset linearZ1D Parabolic optical confine Vin x piz mrp2 z p is the frequency of the ment with linear Zeeman optical confinement and po shift and a spatially homoge defines the magnetic field neous magnetic field in one strength dimension Special parameters to treat ultracold atoms in an optical cavity To deal with a system of bosons i
2. 40 22 Structure of the Entropy dat Mle 1 Kay Hay Saw OES A ee ee SD Sao 40 23 Structure of the TwoBody_Entropy dat file o aa a 40 24 Structure of the lt time gt N lt N gt M lt M gt x correlations dat and lt time gt N lt N gt M lt M gt k correlations dat e a 41 25 Structure of the lt time gt N lt N gt M lt M gt x correlations dat and lt time gt N lt N gt M lt M gt k correlations dat fo Eh Sete ob Sh Sb Ee le ee ee Ek od BS 41 26 Structure of the lt time gt N lt N gt M lt M gt lt x k gt corr lt 1 2 gt restr dat files 41 27 Structure of the lossops_N2_ lt border gt dat files 0a aa aa 42 28 The structure of the lt time gt N lt N gt M lt M gt lt x k gt lt Slice 1 gt lt Slice 2 gt correlations dat Low ae ee eae en be ed ues Cee ee eee eee 42 29 The structure of the lt time gt N lt N gt M lt M gt lt x k gt SkewCorrelations dat files 42 30 The structure of the lt time gt N lt N gt M lt M gt phase dat files 42 1 INSTALLATION 1 Installation 1 1 Prerequisites for the main program The prerequisites to install the MCTDH X program are Fortran compilers Intel PGI or GNU Fast Fourier transforms need to be provided by either Intel MKL or FFTW libraries An FFTW source is included in the package and will be compiled during the installation if FFTW is selected LAPACK routines also have to provided as a library either within the Intel MKL or if selected an included
3. 00 000 e enue 1 2 Prerequisites for full functionality 6 2 Sey onde we hse we oR we wee 2 4 1 3 Running the installation An MCTDH X Tutorial 2 1 Computing an Eigenstate by Relaxation 2 0004 2 2 Computing the Time Evolution of aSystem 2204 3 Program Structure 3 1 Main Program 3 2 Analysis Program 3 3 SCriptS gt r goat a amp pa Guantum the MCTDH X GUI 4 1 Thetabs 4 2 What Guantum Can Do 5 Input File driven Usage MC TDH X 5 1 Defining the Hamiltonian 5 2 Running the computation and analysis 2 2 eee a 5 3 Available Visualization beripts 5 4 4 44 e805 4246s 0b eG ewe 5 4 Configuring the Monster Seript 444224444 64624 bo ee eee ee Slaw 6 MCTDH X output documentation 6 1 Main program output 6 1 1 Output structure in standard MCTDHX computations 6 1 2 Output structure in multilevel MCTDHX computations 6 2 Analysis program output 7 Developer Guidelines 8 Version Management 10 11 11 11 12 12 14 17 17 20 33 34 37 37 37 37 39 42 43 List of Figures 1 Output of an MCTDH X computation in the shell oaa aaa a 8 2 Visualization of MCTDH X relaxation using gnuplot The density p a and the first two natural orbitals 6 x and gS x are shown as red green and blue line respectively ope rece eke 2 eek oe bo bg eae Ae ee De REE
4. Numerically Exact Many Body Dynamics of Indistinguishable Particles USER MANUAL Contact mctdhx ultracold org Download and Support http ultracold org forum by Axel U J Lode and Marios C Tsatsos Abstract This document is intended to guide any potential user to the installation and use of the MCTDH X program package MCTDH X is a highly efficient numerical algorithm to solve the many body interacting Schrodinger equation The present manual describes the basic philosophy and structure of the program and the workflow of the MCTDH X package In particular it explains how to operate and control the main program and the analysis rou tines from the respective input files In addition the graphical user interface Guantum a Java swing application is presented Guantum allows the easy manipulation of the input files and hence the MCTDH X package from a graphical environment The output of the main program s numerical computations is visualized with bash scripts as images and video files with any desired plotting or data processing program A description of the usage of pre defined scripts is included in the present manual Multiple computations such as parameter scans can be automated with the provided Monster script Finally Mercurial the version management system is described and development and good programming guidelines are suggested Contents 1 Installation 1 1 Prerequisites for the main program
5. Column 7 3N Ne amp 8 3N Column 8 3N Ncr 2MN amp Nor to 7 3N Nor 2M N amp 9 3N 4 No 2M N to 8 3N 8 3N Nor 2MN Nor 4MN amp 94 3N Nex 4M N Oey 24 for i 1 N and NO ay 2 t for i 1 N k 1 M and k 1 M 9 Table 19 lt time gt orbs dat file structure for multilevel computations This table explains the column structure of the lt time gt orbs dat output files of the main or analysis program for the case that Multi_Level T was set M is the number of internal states and Noy is the number of conical intersections Nc 0 if Conical_Intersection F Please note that the index of the internal state is always running first before the orbitals index x y z are the spatial coordinates V z y z t is the one body potential of internal state i V y z t is the coupling of the i th conical interaction p x y z t is the density in working orbitals for internal stat i Pwo x y z t is the density in natural orbitals for state i 4 z y z t to x y z t are the working orbitals in internal state i and pRO an y zit to gn x y zt are the natural orbitals in stat i Please note that some of the quantities are complex numbers which then are output decomposed in their real and imaginary parts in two columns as specified by the column numbers 6 2 Analysis program output The output of the MCTDH X analysis software is tog
6. Real default 8 0 starts zfinal Where the spatial grid in Z dimension Real default 8 0 stops Integration Namelist Time_Begin Time at which the simulation shall Real default 0 0 start Time_Final Time at which the simulation shall Real default 20 0 stop Time_Max Maximal time Real default 1 d99 Output_TimeStep Times at which orbital output shall be written Real default 0 1 Output_Coefficients Multiple of Output_TimeStep at which coefficient output shall be written Real default 1 Integration_Stepsize Stepsize of the integration scheme for relaxation this is fixed for propagation this is adaptive Real default 0 01 Error_Tolerance Error tolerance for the integration scheme Real default 1 d 9 Minimal_Occupation Minimal occupation for not consider ing an eigenvalue as 0 in the inversion of the density matrix elements Real default 1 d 12 Minimal_Krylov Minimal size of Krylov basis for coef ficients integration Integer default 4 Maximal_Krylov Maximal size of Krylov basis for coef ficients integration Integer default 20 Orbital Integrator Integrator for the orbital equations of motion Character ABM or OMPABM means that OpenMP parallelized Adams Bashforth Moulton predictor corrector inte grator is used BS means Bullirsch Stor RK means Runge Kutta and STIFF means ZVO
7. The script offers several configuration options like different platforms Generic mpif90 CrayXC40 and compilers Intel GNU PGI ftn On a new platform a modification of the Makefile or scons script might nevertheless be necessary If the Generic build option is selected the build is performed with gfortran and the included OpenBlas and FFTW sources The mpif90 option will use either mpif90 or mpif90 openmpi for the build and the CrayXC40 option se lects the Makefile hornet for the Cray computer Hornet and uses the Cray Fortran compilers ftn To get further information if you are not at all familiar with GNU make and the build on your platform fails contact and seek help at mailto mctdhx ultracold org or in the forum http ultracold org forum The installation script creates a few aliases and appends to the PATH environment variable It creates a file mctdhxrce and guantumrc and appends to the bashrc to source the mctdhxrc such that the new commands become available Available commands aliases are collected in the following table MCTDH X 5 2 AN MCTDH X TUTORIAL Alias What it does cdm takes you to the MCTDH X installation directory mcg sh lt X gt MCTDH X code grep Script which parses the MCTDH X code for the argument lt X gt data_miner sh run an interactively configured analysis on computations in all subdirecto ries MCTDHX executes the the program for interactive use only Mos
8. of subroutines variables or modules should start with a capital letter For subroutines and modules their action s are prefixed with an underscore like for instance Get_KineticEnergyAction_AllOrbitals update this manual with new functionality and user guidance add code documentation that doxygen can process i e start commented lines with gt or lt This is especially crucial for new subroutines such that other users are able to understand how your routine works and may use or further develop it share your version by commiting it to your working copy and letting the developers know such that your development branch can be merged and tested to enter the next release of the package see paragraph on the version management below use the test script testMCTDHX sh to test your developments against reference values Version Management The tool that is used to manage the development of the MCTDH X software is Mercurial in terminal hg It is available on most Unix based systems and facilitates the contribution of multiple developers to a project Mercurial is a distributed version management system i e each user of it has the the full version history available locally The basic operations are collected in the following list 1 2 3 4 5 6 T 9 making a full copy of a repository with hg clone lt repository location gt creating branches with hg branch lt branch name gt showing a summary of t
9. x button on top left of the window or MCTDHX_gcc MCTDHX_pgf if you have chosen to use GNU PGI Fortran compilers 14 4 2 What Guantum Can Do 4 GUANTUM THE MCTDH X GUI Guantum for R MCTDHB Guantum for R MCTDHB File Tools Help File Tools Help Main Potential Grid amp Interaction Advanced Main Potential I Grid amp Interaction I Advanced Choose DVR method Begin calculation at time t_ini 0 0 Harmonic oscillator Sinusoidal FFT O Exponential Finish calculation at time t_fin 20 0 Print data every At 1 0 Define grid Print Cl data every multiples of At 1 0 xin 16 0 xfin 16 0 No of grid points 128 Initial time step for relaxation 1 0d 1 y_in 16 0 yfin 16 0 No of grid points 128 Error of Integration for orbitals and coefficients 1 0d 9 zin 16 0 zfin 16 0 No of grid points 128 Minimal occupation allowed 1 0d 12 Minimal Krylov subspace 5 Maximal Krylov subspace 40 Integration order 8 Integration maximum stepize 0 01d0 Time error scale 1 d0 Choose the type of interaction Coefficients integrator DAV Contat Gaussian Harmonic Lennart Orbital integrat RK Width of Gaussian interaction 0 25d0 5 a on saa pr 2 H ad Diagonalize first the one body Hamiltonian False v Write ASCII output data True k A Modify here initial state NOTE If checked you need to compile og v o le g 0 5
10. OpenBLAS source will be compiled and linked A version of MPI which provides an MPI Fortran compiler wrapper such as mpif90 is also a prerequisite For the successful com pilation of the included Mercurial version management python development headers have to be installed on the system In Debian based Linux distributions just install the packages gfortran libopenmpi dev openmpi common with your package software management In Ubuntu for in stance you may do the following in terminal sudo apt get install gfortran libopenmpi dev openmpi common 1 2 Prerequisites for full functionality To make the MCTDH X software fully functional the following packages are needed python libpython dev scons gnuplot mercurial mplayer2 mencoder openjdk 7 jre With these packages the integrated software management of the MCTDH X package its GUI and its visu alization movie scripts should be fully functional In Ubuntu for instance you may type the following in terminal to install the prerequisites sudo apt get install python libpython dev scons gnuplot mercurial mplayer2 mencoder openjdk 7 jre 1 3 Running the installation After the prerequisites are fulfilled to install MCTDH X one has to first unpack the program package this unpacking can be skipped when you download from the repository with hg clone tar xvf mctdhx tgz Subsequently the program can be installed by running the interactive installation script Install_MCTDHX sh
11. Real default 0 d0 tensity is decreased linearly to 0 d0 Pump_Oscillate Does the pump power oscillate Logical default F as esin w t when it reached the plateau in the exponential ramping procedure Pump Amplitude Amplitude e of the oscillation Real default 0 d0 of the pump power in units of Cavity_PumpRate Pump_Period Period wp of the oscillation of the Real default 0 d0 pump power X_Cavity_Pump_Waist Gaussian envelope s width for pump Real default 0 d0 laser for two dimensional systems Cavity_Mode Waist Gaussian envelope s width for cavity Real default 0 d0 mode in two dimensional systems Special parameters to treat atoms in optical lattices MCTDH X offers two ways of dealing with atoms in optical lattices Lattice Hamiltonians can be treated using an exact diagonalization treatment for one two and three dimensional lat tices Especially in the two and three dimensional cases the dimensionality of the Hilbert space and the matrix that has to be diagonalized in the exact diagonalization approach is exploding rapidly and the problem size can no longer be handled For the larger systems one has to use the so called MCTDBH approach where the Bose Hubbard Hamiltonian is expanded in a multi configurational basis with a number of effective single particle states than there is lattice sites With this approach a systematic improvement beyond mean field theories such as the discre
12. and produce a time series of images Subsequently this time series of images is encoded as a movie file using mctdhx_mencoder mctdhx_gnuplot and mctdhx_mencoder are installed on your platform from the source tarball in the subdirectory External_Software by the MCTDH X installation script The automated way of using the visualization scripts is through the visualization master script The Visualisation Master Script vms sh is a short bash script that can be used to conveniently facilitate the creation of videos from a computation s data To use vms sh just run it with the command vms sh lt Movie Type gt lt Computation directory gt lt Lower plot range gt lt Upper plot range gt lt Gridpoints gt lt 2D Slice 1 gt lt 2D Slice 2 gt where Movie type is one of the scripts in the Visualisation_Scripts directory If Movie type all is specified all available movie scripts will be run for the particular computation The computation directory must contain the input file MCTDHX inp of the computation The other arguments are optional and need not to be given They can be used to fine tune the output of the analysis program i e the plotting range the gridpoints and the slices for the output of the corre lation functions of two dimensional computations If you need to find out the valid strings to use then run the command vms sh and list of the available strings will be output to the screen If the command vms sh lt Movie Type
13. potentials are also specified in the html documentation and the ex ample input in the directory Input_Examples If a custom interaction potential is desired this has to be implemented in the Get_InterParticle_Potential F routine The table 5 1 shows the predefined interparticle interaction potentials as well as how to configure them with the input file s parameters Defining the initial state Y The MCTDH X wavefunction is a multiconfigurational expansion with time dependent coefficients C t and time dependent configurations r t In order to fully define the wavefunction lve So Ca 1A5 t 2 ii one has to define all coefficients Cz and all configurations t In the case of a fully user defined guess i e GUESS HAND in the input file the wavefunction is supplied via Fortran routines The coefficients are defined in the file source ini_guess_pot Get_Initial_Coefficients F and the orbitals from which the configurations are built are defined in the file Get_Initial_Orbitals F in the directory source ini_guess_pot Both contain a single Fortran subroutine that assigns the corresponding array for a documentation of the routines please see the html documentation For a relaxation i e the calculation of a certain eigenstate of the many body Hamiltonian H usually it is a good choice to start from a Gross Pitaevskii i e single configurational state with N 0 0 For a propagation there is also the possibi
14. run MCTDHX_analysis process ASCII data with gnuplot Steps 1 through to 3 are done with the main program and step 4 is done with the analysis program and movie bash scripts There is several ways of automatization of the above 4 step scheme As mentioned above there is a scripts called Monster sh in the Computation_Scripts directory that allows a fully integrated and automated processing of whole series of computations Finally the data processing to videos is automated in the visualization master script vms sh 5 1 Defining the Hamiltonian The Hamiltonians that can be treated by the MCTDH X package in its current implementation are those with maximally two body operators In general such a Hamiltonian hence contains the kinetic energy and the external potential V and an interparticle interaction W N N H S Gj Vi X Wy 1 i 1 i lt j 1 To fully define this Hamiltonian in dimensionless units see Phys Rev A 77 033613 2008 one has to define the one body potential V and the two body interaction W It has to be stressed that both operators can be in principle time dependent 5 1 Defining the Hamiltonian 5 INPUT FILE DRIVEN USAGE MCTDH X Specifying the one body potential V The one body potential V is specified in the file source ini_guess_pot Get_1bodyPotential F This file contains a single Fortran subroutine with a case selection for the dimensionality of the treated problem The potentials defined in this ro
15. running the main program to compute a many body eigenstate as well as to compute a time evolution for bosons after changeing the potential Subsequently the analysis program is run to extract some quantities of interest that then are visualized with the included bash scripts to obtain videos of the computed dynamics 2 1 Computing an Eigenstate by Relaxation After the installation script has finished you should make sure that the aliases and links are working To do so first type source mctdhxrc ls MCTDHXDIR Now you should see the executables MCTDHX_ lt compiler gt MCTDHX_analysis_ lt compiler gt and the library libmctdhx so If you don t the installation did not terminate correctly and you should 2 1 Computing an Eigenstate by Relaxation 2 AN MCTDH X TUTORIAL check what went wrong see the log files created in log and contact the developers in case you cannot find out or fix the error To get started it s best to create a directory for the tutorial computations mkdir MCTDH X Tutorial cd MCTDH X Tutorial To copy all necessary files to run the computation in this directory we make use of the alias inpcp and libcp which copy the example inputs MCTDHX inp analysis inp and the dynamic library libmctdhx so to the current directory libcp inpcp ls The 1s command should show a list including MCTDHX inp analysis inp and libmctdh so With these three files we re able to run the main and analysis
16. the program is the timeline of these commit messages and they are therefore crucial to let the other users and programmers know about changes Share the changes After your local revision is prepared you can share the changeset by contributing it to the main repository by running hg push which will prompt you for username and password If you get a message that notifies you of the creation of a remote head please contact the developers at mctdhx ultracold org since it s likely that there is a conflict between your changeset and the latest revision in the repository In that case it is necessary to merge the heads and resolve the conflicts Feedback and suggestions as well as bug reports are welcome anytime at mctdhx ultracold org or http ultracold org forum
17. 14 15 16 17 Column 1 Column 2 to 1 M Column 2 M Time t Natural orbital oc Energy E t NO cupations p t to NO aed Table 13 NO_PR out file structure This table explains the column structure of the NOPR out file M stands for the number of orbitals in the computation 6 1 2 Output structure in multilevel MCTDHX computations For the case that atoms with internal structure are treated Multi_Level T the column structure of the ASCII output files is described in the following tables 18419 The structure of the output files described in tables 14 15 17 is identical for multilevel compu tations M 6 1 Main program output 6 MCTDH X OUTPUT DOCUMENTATION Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8 N of in Time t Eora t Pogo rat Ecr t Ectyrei t Etot t Ey t tegration step Table 14 Structure of the Error dat file This table explains what is saved in the different columns of the Error dat file E t and Eorvrei t are the absolute and relative integration errors from the orbitals equations of motion respectively Eoz t and Ecy ei t are the integration errors from the coefficients equations of motion respectively Eyo t Foro t Ecr t is the sum of the orbital and coefficients integration errors and Fy t it an experimental error measure for the error due to a time dependency of
18. AHAHRHAHHRERAAHARHERRRRARARRAHERERRHRAARERRRRARERRARARRRRRRR ARERR RRR HERHHHHHHHHRHHHRRHHARAHARRRHAARRA RARER HHHH I USE THE FFTW FFT LIBRARY HHHHHHH HEHHHHHHHHAHHHEHHHHARHHAHRRHHARRAHARRRARRR BARR Memory allocation is ok Binary files properly opened Headers written to Binary file OLD_MCTDHB_COEF inp Headers written to Binary file OLD_MCTDHB_ORBS inp Time 0000000000000000 Step 0 10000000000000001 Energy 309 85823158476620 Time 5 0000000000000003E 002 Step 1 0000000000000000E 002 Energy 287 08103302036045 20 00000000rbs dat u 1 8 u d3 sqrt 24 2 u t3 sqrt 222 16 6315 9 0736981 Figure 2 Visualization of MCTDH X relaxation using gnuplot The density p x and the first two natural orbitals gn x and gn x are shown as red green and blue line respectively MCTDH x 2 2 Computing the Time Evolution of a System 2 AN MCTDH X TUTORIAL tail n 1 NO_PR out We get 20 00000000000031 0 5453108642221355E 02 0 1164565131824607E 01 0 2265201507726221E 01 0 9602492249622707 259 1403195319616 which is the time t the natural occupations oy t a backs pO t and the energy of the system E t in the final column see also table 13 for the structure of the NO_PR out file We conclude that despite the strong interactions of Ay 1 0 our eigenstate of the N 50 bosons in the harmonic confinement is close to condensed since 96 of the bosons sit in the lowest single particle state In the single
19. DE specialized to stiff equations is used default OMPABM 23 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X Orbital_Integrator_Order Order of the integration of the orbitals integrator choice depends on the Inte grator Integer for RK it is 5 or 8 for ABM OMPABWM it is 2 to 8 for BS its 2 to 16 and for STIFF it is 1 or 2 de fault 7 Orbital Integrator MaximalSt Restricts the maximum stepsize in the orbital equations integration Real default 0 01 Write ASCII Specifying wether ASCII files are out put during the computation Logical default T Error _Rescale TD Er time Specifying a scale for the ror Tolerance parameter for dependent one body potentials Real default 1 0 tials see table LZ Trigger one body angular momentum Logical T or F default F operator in the Hamiltonian OMEGAZ Prefactor of one body angular momen Real default 0 0 tum operator STATE Which eigenstate of the Hamiltonian Integer 1 means the to compute groundstate default 1 Stable for Coeffi cients_Integrator DSL or DAV Coefficients_Integrator Which integrator to use for the coeffi Character MCS means cients equations of motion MCTDH SIL routine DSL means MCTDH SIL diag onalization routine DAV means Davidson diagonaliza tion no defaul
20. LS ES 8 3 Checking the status of an MCTDH X computation with mctdhx_status sh 10 Main first tab of Guantum the graphical user interface of MCTDH X graphical user interface of MCTDH X 2 20 0 0 0 000 eee ee es 15 T The main tab of Guantum j 224 43 a a a8 8 baw a oS S Sew BES Eo 16 List of Tables PE 6 Seui ew Om au eh e Se ee i 19 4 Predefined time independent and time dependent interaction potentials 20 ioe kis oe e ee 25 10 MCTDH X analysis parameters 22 eb ed ae eed eee ede dee ead 32 11 List of available visualization seripts 24 4 24664 a bb e456 eh eed 33 12 Parameters inside ParameterScan inp ooa a 0 00 eee eee eee 37 13 NO PR out file structure os te eee EOS RRS SC 2K SS ERS ew See 37 14 Structure of the Error dat file lt n05 4s ok wwe ee eee ee OLE Oe RRS 38 15 Timine dat file structure 24 44 a e2 Fb bw EER ee Re EEE Ha 38 16 lt time gt orbs dat file structure vee bY a ee aR ee Oe ee Ce eS x 38 17__Structure of the lt time gt coef dat files 2 2 a 39 18 NO PR out file structure for computations with Multi_Level T 39 19 lt time gt orbs dat file structure for multilevel computations 39 20 Structure of the lt time gt N lt N gt M lt M gt x density dat and lt time gt N lt N gt M lt M gt k density dat ee ne ee oe ee eee ee a ee ee ee ee ee 40 21 The nonescape probability output file Nonescape
21. Y coordinate of second posi Logical default F tion momentum F k constant y2slice At which value to keep the Y Real default 0 0 coordinate of 7 k ZEROPADDING2D For 2D Fourier transforms activa Logical default T tion increase of resolution by zero padding DILATION2D By what factor to increase the reso Integer no default lution PROJ_X Calculate effective density one Logical default F dimensional potential Vey J dg Dar pig Q x y t d z y t where x and or y DIR Specifying the direction for the effec Character X means zx tive one dimensional potential Y means y and B means both x and y are computed Lz Computation of angular momentum Logical default F eigenvalue and matrix elements Table 10 MCTDH X analysis parameters This documentation of the variables in the analysis inp is also available in the html code doc umentation and the in line documentation of the example file After an appropriate modification the program can be run in an interactive shell by typing MCTDHX or by using adapting submitting one of the example PBS scripts in the PBS_Scripts directory and submitting the computation into the queue of a job scheduling system The analysis can be run after a computation has finished and the modification of the analysis inp file with the following command MCTDHX_analysis After the analysis
22. a full explanation of the structure of this file see table In figure 2 you can see a screenshot of what your gnuplot output should look alike To find out the occupations of the natural orbitals let s have a look at the last line of the NO_PR out file 2 1 Computing an Eigenstate by Relaxation 2 AN MCTDH X TUTORIAL Initialization M over N and N M 1 over N 0000000000000000 23426 000000000698 allocation ok for DVR_Parameters allocation ok for Matrix_Elements HHHHHHHHHHHHHRHRHAHHRHRRRRRR RRR HHH INPUT READ AND DISTRIBUTED HERHHHHRHHHARHHARRHHARRHARRRH HARRAH HHHHHHRHHHARHHHRRHHARRHHRRRHHARR RRR HHH COEFFICIENTS INITIALIZED HHH HHHHHHHAHHAHEHREHHAHHRHAHRRRRR RRR HHHHHHHHHHHHERERHAHHRHRHRRRRR ARBAB RR RHR DVR INITIALIZED RHR HHRHHHHRHHHARHHHRRHHARHHARRR HRA R RRR HHHHHHHHHHARHHHRHRHHARHHAHRRRHARRBRR RB INTERPARTICLE POTENTIAL INITIALIZED HHHHHHHHHHAHERARAAHHRHRHRRRRR RRR HERHHHHRHHHARHHARRHHARRHA RRR PROCESS IS THE MASTER PROCESS HERHHAHHHHARHHARRHHARHRHRRRRHHARRR RRR HERHHAHHHHAHHHARHHHARHRHARRRRHARHRAEARHRRARRRRARRAARR HARRAH HARA AAR RR RRR RRA RH EGEEEEEEE GGEGEE CACAO GGCECEE CGC CG CAAMA EGEEEEEEEE CACAO CAAA EGEEEGECE CEE COA CACC 0e ce e ece ec eee ee eee 1 tQ 1 1 1 e le LI FL1 L oar LN 1 off PLI LII LIQNI Wis st Ii Ll ost EE 0S 000 EN ete RHHHHH
23. and preparing the run files An example input file can be found at Input_Examples ParameterScan inp which contains in line documentation see 12 Inside the working directory one must place a properly configured ParameterScan inp libmctdhx so a binary executable file consistent with binary defined inside ParameterScan inp and an input template consistent with Input_Template defined inside ParameterScan inp Once these 4 files are properly configured and placed the script is called by running MCTDHXDIR Computation_Scripts Monster sh The script scans up to 5 user defined relax ation parameters runs them until convergence is detected and if desired automatically scans each relaxation with up to 5 user defined propagation parameters When running on a cluster the script will automatically restart jobs if they finish due to time constraints before the calculation 7 5 4 Configuring the Monster Script 5 INPUT FILE DRIVEN USAGE MCTDH X is complete To circumvent job number restrictions on clusters the script will build a series of runscripts that each simultaneously run many calculations in a single job rather than a single computation per job A little under the hood knowledge is useful to to effectively use and debug Monster sh The script initially calls MCTDHXDIR Computation Scripts ParameterScan Propagation sh or MCTDHXDIR Comptuation Scripts ParameterScan Relaxation sh depending on the input file configuration which then iter
24. articles N the strength of the interaction and the particle mass see Fig Furthermore you can choose to solve the stationary imaginary time propagation or the time dependent real time propagation Schrodinger equation or even propagate in reverse time Check the box Include rotation to include the effective rotation term L in the Hamiltoniarf Check the box Send me e mail and add your e mail address to the textfield to be notified about the status of your computation and receive a preview of your results directly to your e mail Second Tab On the second tab you can choose any of the six preset types for the spatial confinement of the atomic gas i free space ii harmonic parabola iii lattice iv double well v parabola with a rotating anisotropy and vi parabola with a rotating Gaussian thread see Fig When you click on each of them you immediately see the form of the potential with red highlighted the parameters that determine the selected potential trap and need to be defined Below this form the textfields to define the corresponding parameters appear The Guantum will automatically set the dimensionality of the potential according to the choice of dimensions D on the first tab Last if you need to give some other form for the external trapping potential you can do so by clicking on or type any other form and click on Compile On the text field appearing on the bottom you can write the desired functio
25. ates through the corresponding parameter set As the script loops through each parameter set it calls either MCTDHXDIR Scripts IterateParameters sh or MCTDHXDIR Scripts IterateParameters_relax sh which then perform the actual secretary functionality using about a dozen smaller scripts inside MCTDHXDIR Scripts If it is determined that a new calculation must be run when using a cluster a few lines are added to a runscript in the working directory called run sh for some number To avoid duplicate computations a file in the computation directory is created called RunFlag which is automatically deleted when the job runs out of time or the computation is complete via some code within the runscript The runscript accumulates calculation jobs until the total number of nodes requested reaches a threshold defined by MPMDNodes in ParameterScan inp and then it is submitted using a qsub command within either MCTDHXDIR Scripts MPMDrun_relax sh or MCTDHXDIR Scripts MPMDrun_prop sh on line 106 It is often useful to comment this line for testing purposes as it will prevent the script from submitting any jobs leaving it to only copy move and edit files Directories with incomplete calculations are stored in files Relax_Array and Prop Array Directories are removed from these files when their corresponding calculations are complete triggering an end of the corresponding ParameterScan_ sh function call when the array is empty When Monster sh is run wit
26. atus Click on check results button on the very bottom of the GUI and the windows resizes itself The Plot Refresh job status button will run the mctdhx_status sh script create an image of the status of the calculation and print it inside Guantum If there are no output files an error message will inform you of Otherwise after some seconds you should see a plot of the energy and fragmentation in time real or imaginary depending on the type of calculation as well as the the total density of the gas at the latest time step that has been calculated so far File Tools Help Main Potential Grid amp Interaction Advanced ll T 4 f Video settings E 3 7 ee f hav HY H T V gW Type of video e c Everything x Choose number of dimensions D Ol O2 03 1 Density Plot range from to s 5 No of orbitals M 3 0 9 5 0 8 No of particles N 12 No of plotpoints E 1024 Strength of interaction flo io Particle mass m 1 0 g Compile movies D Type of Schroedinger equation to be solved Stationary Propagation Backward propagation Include rotation Ho L 9 only in 2D Send me e mail notification when results are ready i A ao EA 20 25 30 35 40 45 x State to be calculatedn 1 v Time Cuaaton heme eden Choose file P AAFPAD Af Plot Refresh Animate gt job status
27. current version second make sure if the changes you want to share as a contribution to the main repository are there and which files are affected third commit the changes as a new revision to your local repository and write a thorough description of the implemented changes and fourth push the changeset to the main repository Create branch To create a branch run hg branch lt name gt Typically lt name gt should be your user name in the forum or descriptive for the features that are planned to be developed in this branch Clean up To remove the compiled included software run make f lt Makefile your configuration gt purge and then to remove the objects and libraries generated in the compilation of the main pro gram run make f lt Makefile your configuration gt clean Inspect the changeset Check if indeed only the files that you intended to modify show up when you run hg status If unsure look through the individual files and in case of doubt recompile reinstall the program and test it again for instance by running testMCTDHX sh and start over with the first step Commit revision Once you verified and tested your changes commit them to your local repos itory by hg commit u lt username gt After issueing this command you will be prompted to write a so called commit message The text should include a brief but concise description of the changes entering the revision and a list of open tasks or known problems The changelog of
28. d ramp down time of the anisotropy p4 plateau time at which Pa P2 stir2D 2D harmonic trap with ro V x t p stirring fre tating stirring rod e pcos p t y p2 sin p1t quency po stirring radius p3 height of Gaussian rod p4 width of Gaussian rod Table 3 Predefined potentials and parameters a previous one by specifying GUESS BINR in the input file 19 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X Which Interaction Description Potential and Interaction_Type gauss and 1 2 3 4 Gaussian interparticle W r rT o ger I interaction of width Interaction Width 0 Contact interaction with W F T Ao r 7 constant strength Ao I cos and 6 Contact interaction with W 7 7 Xo cos 1t 6 7 7 time dependent strength A t sin and 6 Contact interaction with W r r XAosin 4t do 7 7 time dependent strength X t TDHIM and 5 Time dependent version of W F r Ao 1 0 4sin t F r the harmonic interaction model TDegaussl and 5 Gaussian interac W r r o tion with width L sin Dt erp 5 Interaction Width o and time dependent ampli tude TDgauss and 5 Gaussian interac W r r Xo tion with width xp Interaction_Width oO at t O that is
29. e body den Logical default F sity in space Density_k Output of diagonal of one body den Logical default F sity in momentum space Fast_FFT Use MKL or FFTW FFT in the Logical default T analysis Pnot Computation of nonescape probabil Logical default F ity Prot xstart Where does the integration on the Real no default density for Paot start xend Where does the integration on the Real no default density for Paot stop ystart Where does the integration on the Real no default density for Paot start yend Where does the integration on the Real no default density for Paot stop zstart Where does the integration on the Real no default density for Paot start zend Where does the integration on the Real no default density for Paot stop Phase Computation of the phase Logical default F Gradient Computation of the phase gradient Logical default F Entropy Computation of diverse entropy Logical default F measures NBody_C_Entropy Computation of entropy of full N body density matrix Logical default F TwoBody_Entropy Computation of entropy of 2 body density matrix Logical default F Cavity_Order Computation of cavity order param eter Logical default F TWO body Correlations_X Computation of spatial correlation functions on the full grid Logical default F Correlations_K Computation of momen
30. e names of the files lt time gt is the time t lt N gt is the particle number lt M gt is the orbital number The generation of these output files is triggered by setting Density_X and Density _K to T respectively Column 1 Column 2 Time t Nonescape probability Prat Ts e Table 21 The nonescape probability output file Nonescape If the input variable Pnot and the borders x and x were defined with xstart and xend in the input of the analysis program this file is created Column 1 Column 2 Column 3 Column 4 Time t Sp r t Sp klt Sc t f dro r t In p 7 t f dkp k tJin olk t Xa lren CaA Column 5 Column 6 Column 7 Sn t 1 S t nS sere IUR Cia t Inf Cie t 7 Table 22 Structure of the Entropy dat file The last column is only present if NBody_C_Entropy T is set in analysis inp Column 1 Column 2 Column 3 Column 4 Time t S 2 r t Geet S co t f dr drop Fi Fa t l oP idkap P ky kz tbh gO ED 2 penne N Table 23 Structure of the TwoBody_Entropy dat file i 6 2 Analysis program output 6 MCTDH X OUTPUT DOCUMENTATION Column 1 Column 4 Column 7 Column 8 5 i 1 amp Column 10 to 3 to 6 5 i 1 9 5 i 1 5 i 1 T Y Z or x y 2 or pil Y zit o x y z 2 y 25t or plz y zt Kes Ry hs Ry Rig hy 1O P ko k
31. ead if GUESS DATA Character no default DVR Namelist DIM_MCTDH Specifying the dimensionality of the Integer 1 2 or 3 default 1 problem NDVR_X Specifying the number of DVR func Integer default 256 tions in X dimension NDVR_Y Specifying the number of DVR func Integer default 1 tions in Y dimension NDVR_Z Specifying the number of DVR func Integer default 1 tions in Z dimension DVR_X Which DVR will be used in X direction Integer 1 means harmonic os cillator DVR 3 means sine DVR 4 means FFT DVR and 5 exponential DVR default 4 DVR_Y Which DVR will be used in Y direction Integer 1 means harmonic os cillator DVR 3 means sine DVR 4 means FFT DVR and 5 exponential DVR default 4 DVR_Z Which DVR will be used in Z direction Integer 1 means harmonic os cillator DVR 3 means sine DVR 4 means FFT DVR and 5 exponential DVR default 4 x_initial Where the spatial grid in X dimension Real default 8 0 starts x_final Where the spatial grid in x dimension Real default 8 0 stops 3Fast Fourier Transform Discrete Variable Representation 22 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X y_initial Where the spatial grid in Y dimension Real default 8 0 starts y_final Where the spatial grid in Y dimension Real default 8 0 stops z_initial Where the spatial grid in Z dimension
32. f potential V r b Free Space Harmonic Lattice Double Well Parabola Rotating Rotating Thread or type any other form and click on Compile e g 0 5x 2 0 3 y r4 Compile Figure 5 Potentials second tab of Guantum the graphical user interface of MCTDH X on the current Guantum version are provided 4 2 What Guantum Can Do Creates and Saves MCTDH X Projects and Submits Performs Computations 1 Guantum creates the MCTDH X input file depending on the parameters you specify every thing is printed on a MCTDHX inp file exactly as required from the MCTDH X package The file is created at the moment you click on GO button 2 When you first open the program the current working directory is path to mctdh x Guantum_Files tmp There by default the following files exist a b c libmctdhx so and MCTDHX_intell so that you need not compile the program unless you type in a customized potential on the second tab mctdhx_status sh the scipt to produce density and fragmentation vs time and energy vs time images and vms sh the script to create the video files once there are output dat files When you exit the program everything in the tmp directory except these four files is deleted To exit Guantum simply click on File Exit or alternatively use the keyboard shortcut Ctrl Q or just click on the
33. fied the library has to be re compiled and copied to the computation s directory Recompiling the library libmctdhx so is conveniently achieved by issueing the command libmake After compilation the library can be copied to the working directory by typing libcp Finally the input files should be copied to the working directory This can be done by typing inpcp The two files MCTDHX inp and analysis inp are now inside the working directory The details of the input variables in those files can be taken from the in line documentation in the input file or the html code documentation The MCTDHX inp file basically contains variables like the particle number the number of orbitals the dimensionless interaction strength number of primitive basis functions their type details of the integration integrator stepsize accuracy order and many more See table 5 for all currently available parameters in the main program and their meaning System Parameters Namelist Parameter Meaning Options JOB_TYPE Select problem i e MCTDH for Character BOS FER bosons MCTDH for fermions or TDCI for bosons FOT FER still buggy Default BOS Morb Select number of time dependent vari Integer no default ationally optimized basis functions Npar Select number of structureless parti Integer no default cles xlambda_0 Adjust prefactor of two body potential Real no default i
34. gled with the input file analysis inp as Laina described in the table Generally there lkiads of different output file structures Some 6 2 Analysis program output 6 MCTDH X OUTPUT DOCUMENTATION analysis quantities are scalar and their time series will be saved in a single file like e g the nonescape probability and some other quantities need one file per point in time like e g the density or momentum density Orbitals_Output and Coefficients_Output toggle the output of the files lt time gt orbs dat and lt time gt coefs dat their structure is the same as when one sets the variable Write_ASCII in the main programs input to T see tables 16 and 17 In the following tables 20 21 25 24 26 2 7 28 29 22 23 and 30 the structure of the output files generated by setting the respective analysis variables is given Column 1 to 3 Column 4 to 3 M cP OF ky ky kz po a y z t or alm ky kz t Table 20 Structure of the lt time gt N lt N gt M lt M gt x density dat and lt time gt N lt N gt M lt M gt k density dat files x y z and kz ky kz are the spatial and momentum grid respectively N is the number of internal states and p x y z t and p k ky kz t are the spatial and momentum densities respectively In the case of a computation treating atoms with internal structure the index 7 runs through all internal states of the considered atoms and one density is output for every state In th
35. gt lt Computation directory gt is entered successfully it will generate all the ASCII data from the binary MCTDH X output and build the movie s All the visualization scripts in the Visualization_Scripts subdirectory have five command line argu ments timeInitial the time at which the movie will begin timeIncrement the time difference between each frame timeFinal the time at which the movie will end MOrbs the total number of orbitals in the simulation and Npar the number of particles in the simulation vms sh basically calls the respective desired visualization script s with the appropriate arguments Eventually it prints a short message And we are happy once the video has been successfully created Of course one can also call the scripts in the Visualization_Scripts directory manually by typing lt Visualization_Script gt lt timeInitial gt lt timeFinal gt lt timeIncrement gt lt MOrbs gt lt Npar gt where lt Visualization Script gt can be chosen from the list in Table 5 4 Configuring the Monster Script This script basically acts as a secretary creating subdirectories copying files editing text and submitting jobs in a coordinated fashion so that after the user configures just 2 text files a sin gle function call can result in thousands of computers working for days to weeks to calculate up to a combined 10 dimensional paramter scan There are two steps to configuring Monster sh configuring the input file
36. he above terms are present in the Hamiltonian a transfer of population between the different levels of the treated particles is allowed The input variables necessary to control the program through the MCTDHX inp file in the case of multileveled or spinor particles are specified in the following table System Parameters Namelist Parameter Meaning Options NLevel How many levels do the considered Integer default 1 particles have Do the atoms have internal struc Logical default F ture Multi_level Logical default F set to T Does the one body Hamiltonian con tain terms V 7 that couple differ Conical_Intersection the potential ent internal states VTRAP_EXT which is defined in Get_lbodyPotential F con tains one additional vector that stores Vj InterLevel_InterParticle Does the interparticle interaction couple different internal states di rectly attention this is for mul tileveled atoms which are NOT spinors Logical default F a spin dependent interparticle inter action xlambda lt X gt Interparticle intra level interaction Real default 0 d0 strength for non spinors lt X gt 1 2 3 xlambda12 Interparticle inter level interaction Real default 0 d0 strength for non spinors Spinor Are the treated atoms spinors with Logical default F 26 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X
37. he changes with respect to the last revision by hg status adding and removing files by hg add lt files gt and hg remove lt files gt add all new files and remove all missing files with hg addremove showing the history of commit messages for all revisions by hg log commiting changes made to a revision of the repository as a new revision with hg commit u lt username gt pushing or pulling the changes made in the present repository to another repository by hg push lt repository location gt or hg pull lt repository location gt updating the repository after pulling pushing a changeset by hg update It is important to note here that the version management of the central repository is open for all users hence everyone registered in the forum http ultracold org forum can in principle contribute to the development 8 VERSION MANAGEMENT Contribution how to The strategy taken for the development of MCTDH X is that every contributor should create her his own branch for the software development For collaborative contributions of multiple users branches may also be created with a name describing the respective contribution When a new version is due to be released all the different branches will be merged into the default branch to form a release In the following the basic steps to create branches and to push your current revision into the main repository are described These include to first clean up your
38. hout any arguments all lingering runscripts RunFlag s and arrays are cleared If the user wishes to keep these files they must run Monster sh save Parameter Name Description Values Do_Relax Specifies whether to do or skip relax T F ations Do_Propagations Specifies whether to do or skip propa T F gations Propagation Start Specifies how to start propagations BINR HAND when relaxation is skipped Do_Analysis Specifies whether to do or skip analysis T F MonsterName Sufix for job names MON any string STER_ MonsterName runhost Specifies which cluster is used or if no hermit hornet cluster is used maia bwegrid PC numnodes Specifies number of nodes used for re Integer laxation jobs MPMD Specifies whether to run in Multiple T F Program Multiple Data mode i e mul tiple computations per submitted job This only applies to scans on a cluster and is recommended if more than 20 computations are desired 35 5 4 Configuring the Monster Script 5 INPUT FILE DRIVEN USAGE MCTDH X ing directory MPMDjobs If using MPMD mode this specifies Integer how many nodes are requested for each job maxjobs Maximum number of jobs allowed on Integer the queue 20 for hornet and hermit binary Name of MCTDHX executable in work usually MCTDHX_intel Input_Templa
39. iggers the program to do a forward time propagation GUESS BINR will make it read the initial state from the binary files CIc_bin and PSI_bin and Binary Start Time 20 d0 chooses the time at which the binary files CIc_bin and PSI_bin are read for the initial state Now in order to define the parameters specifying the propagation in the double well we change the following variables in the MCTDHX inp Integration_Stepsize 0 0001d0 whichpot h d parameter1 2 d0 parameter2 8 dO parameter3 1 d0 3 PROGRAM STRUCTURE Status of the computation Fragmentation _ 0 9 Energy 487 6293317617653 Density x Fragmentation Figure 3 Checking the status of an MCTDH X computation with mctdhx_status sh The left panel displays the time evolution of fragmentation i e 1 y pW t in the system and the right panel shows a snapshot of the current density Integration_Stepsize 0 0001d0 specifies the initial time step compare table 5 The which_pot h d variable selects a potential which is the sum of a displaced harmonic potential and a discplaced Gaussian barrier in its center To define the potential parameter1 2 d0 is the dis placement parameter2 8 d0 specifies the height of the barrier in the center of the parabola and parameter3 1 d0 gives the width of this barrier After modifying the input we type MCTDHX to run the propagation and wait until it finished After it ha
40. is the density in working orbitals pwo x y z t is the density in natural orbitals m x y z t to o1 2 y z t are the working orbitals and go x y z t to NO ig y z t are the natural orbitals Please note that some of the quantities are complex numbers which then are output decomposed in their real and imaginary parts in two columns as specified by the column numbers r 6 2 Analysis program output 6 MCTDH X OUTPUT DOCUMENTATION Column 2 amp Column 3 Real and imaginary part of the coefficient Column 1 N of Coefficient Table 17 Structure of the lt time gt coef dat files Column 1 Column 2 to 1 Column 2 M Column 3 M Column 4 M M to3 M N N M Time t Natural orbital Energy E t State popula State On patins tions density lations pre t to for all levels orbitals for all pn t levels Table 18 NO_PR out file structure for computations with Multi_Level T This table explains the column structure of the NOPR out file M stands for the number of orbitals in the computation and N is the number of internal states considered Column 1 to 3 Column 4 Column 5 to Column 5 Column 6 4 N Ner Ni Ncr amp 2N Nor amp 6 N Nc to 7 2N Ner 4 2N Ner to 5 3N amp 5 2N 4 Nor amp 64 No1 3N Ncr L Y z DVR weight V a y 2 t x y z t Pwo 2s Y 25 t and Ver y z t
41. lity to restart the computation from r 5 1 Defining the Hamiltonian 5 INPUT FILE DRIVEN USAGE MCTDH X whichpot Description Potential Parameters HO1D 1D harmonic oscillator V x ipr p trap frequency HO2D 2D harmonic oscillator V z y pis2 trap frequency 5 pix pay in a y HO3D 3D harmonic oscillator V x y z pi 2 3 trap frequency p pit poy p32 in v y z h d 1D harmonic oscillator plus V x 3 2 p p diplacement Gaussian central barrier prexp a po height of Gaus sian p width of Gaussian zero No potential V 0 No parameters Boundary conditions determined by the discrete variable representation MQT_ini Rectangular 1D box V x Vie pi barrier width in 0 20 p and V x propagation MQT_prop 0 x 0 20 p MQT_prop Rectangular 1D box barrier V z co V a lt 0 and p barrier width and open space a V x 0 20 p and V x 0 Viz gt 20 and V x 0 05V a 20 p 20 qpl 1D lattice with 2 frequen V x p cos p x pis3 amplitudes of cies amplitudes p3 COS p4x the lattices poy frequencies of the lat tices rot2D 2D harmonic oscillator with V x t s 1_ p the rotation fre rotating anisotropy a t x cos p t quency pa the time ae p t 1 dependent anisotropy Pa t y cos pit pg anisotropy max pe imum p3 ramp up an
42. lues end of scan range for propagation pa rameter Prop_Scan _Start 1 5 if Prop_List F specifies Number beginning of scan range for propagation parameter Prop_Scan _Stop 1 5 if Prop_List F specifies Number 36 6 MCTDH X OUTPUT DOCUMENTATION Prop_Scan _Step 1 5 if Prop_List F specifies Number step of scan range for propagation pa rameter Table 12 Parameters inside ParameterScan inp 6 MCTDH X main and analysis program output docu mentation 6 1 Main program output MCTDH LX has several standard output files and it will generate additional ASCII output if the toggle Write_ASCII is set to true in the input of a computation Specifically standard output is comprised by the files NO PR out Initialization dat Error dat and Timing dat The additional ASCII output is comprised of lt time gt orbs dat and lt time gt coefs dat files these can also be generated after a computation has finished by running the analysis program which processes the binary data files PSI_bin and CIc_bin Set aside the binary PSI_bin and CIc_bin and the ASCII Initialization dat files all the above output files are column formatted ASCII files 6 1 1 Output structure in standard MCTDHX computations For the case that atoms without internal structure are treated Multi Level F the column structure of the ASCII output files is described in the following tables 13
43. n in any dimensions that should however not exceed the dimensions D of the problem Note that the potential has to be typed on Fortran form only After that one Note that this will function only in a two dimensional calculation where the Hamiltonian is defined on the x y plane and an effective rotation along z axis is considered r 4 1 The tabs 4 GUANTUM THE MCTDH X GUI Guantum for R MCTDHB File Tools Help Main Potential I Grid amp Interaction Advanced E e ET lt ih VU HY H T V QW Ot Choose number of dimensions D 1 2 3 No of orbitals M i No of particles N 2 Strength of interaction 10 ra Particle mass m 0 Type of Schroedinger equation to be solved Stationary Propagation Backward propagation J Include rotation Ho L 9 only in 2D C Send me e mail notification when results are ready State to be calculatedn 1 v m Cuaalun roreedron YrAGTRAS tf KS Check results gt gt Figure 4 Main first tab of Guantum the graphical user interface of MCTDH X has to click on the Compile button and wait an average of 15 seconds which of course can vary from computer to computer for the program to compile and copy the necessary libraries into the working directory Third and Fourth Tabs In the two remaining tabs third and fourth you can alter all the rest
44. n interaction with an optical cavity i e a field of photons which in turn generates a one body potential for the atoms through the dipole force special input parameters have been defined These are listed in the following table System Parameters Namelist Parameter Meaning Options Cavity_BEC Toggle cavity treatment Logical default F NCavity_Modes How many modes to take into ac count treating the cavity Integer default 1 Cavity_PumpRate Rate at which the laser is pumping the cavity through the atoms Real default 0 d0 Cavity_LossRate Rate at which photons are lost from the cavity Real default 0 d0 27 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X Cavity_KO Magnitude of the wave vector defin Real default 0 d0 ing the resonance frequency of the cavity Cavity_AtomCoupling Coupling strength of the atomic res Real default 0 d0 onance to the pumping laser fre quency Pump_Switch Is the pumping laser intensity Logical default F ramped up exponentially kept con stant and then ramped down expo nentially RampupTime Time over which the pump laser in Real default 0 d0 tensity is increased linearly up to Cavity_PumpRate RampdownTime Time over which the pump laser Real default 0 d0 intensity is kept constant at Cavity_PumpRate PlateauTime Time over which the pump laser in
45. n the Hamiltonian mass Mass of the particles Real default 1 0 Job_Prefactor Select which direction to propagate the equations of motion in time Complex 0 0d0 1 0d0 Forward propagation 0 0d0 1 0d0 Backward propagation 1 0d0 0 0d0 Improved Relaxation Default 1 d0 0 d0 NProjections Number of times that the projection operator P is applied to the right hand side of the orbital equations of motion Integer default 2 21 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X GUESS Specifying if the initial guess is defined in dat files the rou tines Get_Initial_Orbitals F Get_Initial_Coefficients F or in the binary files CiC_bin and Psi_bin Character HAND means the Get_Initial routines are used DATA means dat files will be read in BINR means _bin files will be read in default HAND Diagonalize OneBodyh eigenfunctions potential in Select to use of the one body Get_1bodyPotential F Logical T or F T only non FFTP DVR 4 i e DVR_X Y ZA4 default is F Binary_Start_Time Define point in time at which the wavefunction is read from binary files in the case of GUESS BINR Real no default Restart_Orbital_FileName Define filename of orbitals to read if GUESS DATA Character no default Restart_Coefficients_FileName Define filename of coefficients to r
46. n two dimensional computations 2D DENSITY_M4 Movie of the density and the first four orbitals in two dimensional computations 2D ORB_AVG_PHASE_DENSITY_Lz Movie of Orbital average phase density and angular mo mentum in two dimensional computations 2D AVG PHASE Movie of the average phase in two dimensional compu tations 2D DENSITY K Movie of the momentum density in two dimensional computations 2D AVG PHASE PHASEGRADIENT DENSITY ENERGY LZ Movie of the average phase phase gradient density and angular momentum in two dimensional computations 2D DENSITY_X Movie of the density in two dimensional computations CI Movie of the CI coefficients nat_occ_loop Plotting the natural occupations of a computation Table 11 List of available visualization scripts All the above scripts take 5 command line arguments start time stop time time increment number of orbitals number of particles To generate a movie of the coher ence on a restricted grid in momentum space one could do 1D CORR1 RESTR K O 100 0 1 4 101 this command would generate a movie for the first 100 time units in steps of 0 1 for an M 4 computation with N 101 particles The visualization master script vms sh automates the usage of the above movie scripts The way in which this is achieved is by first processing the output files of an an MCTDHX_analysis 5 4 Configuring the Monster Script 5 INPUT FILE DRIVEN USAGE MCTDH X run with mctdhx_gnuplot
47. odyPotential is used to compute the on site potential energy offset Both routines can be found in the file source ini_guess_pot Get_1bodyPotential F The input of the analysis program The analysis inp file contains the desired quantities of analysis and specifies for which points in time these are needed and table 10 for all currently available parameters in the analysis program and their meaning Parameter Meaning Options ZERO_body Orbitals_Output Create ASCII orbital output Logical default T FT Orbitals_Output Create ASCII Fourier transformed orbital output Logical default F Coefficients_Output Create ASCII coefficients output Logical default T MatrixElements_Output Output of reduced one body and two body density matrix elements Logical default F HamiltonianElements_Output Output of one body and two body Hamiltonian matrix elements Logical default F 29 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X GetA Partial sums on the two body Hamiltonians matrix elements Logical default F Time_From Time from which to start analysis Real no default Time to Time at which to stop analysis Real no default Time Points Time points in analysis Integer no default ONE_body Density_x Output of diagonal of on
48. of the parameters that are necessary for an MCTDH X calculation exactly as they appear on the MCTDH X input file see Fig 6 In the third tab you can define the DVR method to be used the extension and spacing of the grid and the type of the interparticle interaction The fourth tab collects all advanced parameters involved in a calculation Read the corresponding parts of the present documentation see Table 5 for an explanation of each of the parameters Menu Bar In the Menu Bar at the top of the Guantum window there are three Menu Items File Tools and Help The first Item File includes the New Open Save and Exit options whose functions are described below In the Tools Item few extra options can be found the Compile and the Kill job button The first can be used when for any unforeseen reason the libraries required for a calculation are missing from the working directory or have been corrupted during copying In that case the above button will re compile and copy all the libraries to the working directory The button Kill job will encounter the running MCTDH X jobs and kill them equivalent to job killing from within a shell In the Help Item the MCTDH X documentation and information T 4 2 What Guantum Can Do 4 GUANTUM THE MCTDH X GUI Guantum for R MCTDHB File Tools Help Main Potential Grid amp Interaction Advanced Choose type o
49. p oe pilke ky kz t pilka ky kat Column 11 5 i 1 pP x y z y 2 t or PP Ke ky kalk kl kl t eye Table 24 Structure of the lt time gt N lt N gt M lt M gt x correlations dat and lt time gt N lt N gt M lt M gt k correlations dat files for multilevel computations For the explanation of the filenames see table 20 These files are created if the input variable Correlations X and Correlations K respectively are set to be true The files contain all nec essary quantities to compute the one body as well as the diagonal of the two body normalized Glauber correlation function gf and g respectively for all internal states 7 For instance ig pt wr 24 it VJ pr ai3t pr x4 t by Column 7 x Column 10 e can be plotted as the value of Column 8 Column 9 divided Column 1 Column 4 Column 7 Column 8 amp 9 Column 10 to 3 to 6 x y z or x y z or p x y 2 t or p x y z x y z t or polz y 2z t or kas kuska kakya By Pes Ry Rat 0 Bay Reais kelko kuka D Ros Rays Rest Column 11 pP x y z z y 2 t or pP ka ky kz kl kl kt t x y Zz 1 Table 25 Structure of the lt time gt N lt N gt M lt M gt x correlations dat and lt time gt N lt N gt M lt M gt k correlations dat files For the explanation of the filenames see table 20 These files are created if
50. program terminated successfully ASCII files structured as specified in the file documentation Analysis_output_documentation are in the working directory of the program These files can be visualized using e g gnuplot or any other visualization software for data 32 5 3 Available Visualization Scripts 5 INPUT FILE DRIVEN USAGE MCTDH X 5 3 Available Visualization Scripts The directory Visualization_Scripts contains several bash scripts to process the ASCII output of an MCTDHX_analysis run into mpg or avi movies For a list of the currently available scripts and their function see Table Visualization Script Function 1D CORR1 K Movie of the coherence g 1D CORR2 RESTR X Movie of the two body correlations g on a restricted grid 1D DENSITY_X TIME EVOLUTION PM3D Movie of the density p x t i e 2D plot where the y axis is time 1D CORR1 RESTR K Movie of the coherence g in momentum space on a restricted grid 1D CORR2 X Movie of the two body correlations g 1D CORR1 RESTR X Movie of the coherence g on a restricted grid 1D DENSITY_K Movie of the momentum density p k t 1D CORR1 X Movie of the coherence g 1D DENSITY_X Movie of the density p x t 2D DENSITY_M2 Movie of the density and the first two orbitals in two dimensional computations 2D DENSITY_M3 Movie of the density and the first three orbitals i
51. programs The default MCTDHX inp is configured to compute the eigenstate of N 2 bosons in a one dimensional harmonic oscillator potential with unit frequency and with M 4 orbitals To make things a little more interesting let s change the the number of bosons to N 50 by editing MCTDHX inp and setting Npar 50 in the System_Parameters namelist i e gedit MCTDHX inp Since we re going to compute some dynamics later we use the opportunity to also enlarge the number of grid points and the grid extension in the DVR_Parameters namelist a bit further down in the MCTDHX inp file We set Npar 50 NDVR_X 256 X_initial 12 d0 x_final 12 d0 With these adjustments made we can run the relaxation to the groundstate of the harmonic oscillator potential by typing MCTDHX This should show an output similar to the following figure 1 This computation is going to take a minute so sit back and relax or just get a coffee until it finished The energy you should see on screen in the final propagation step should be identical to 259 14031953196161 up to the last 3 digits To visualize the output let s use gnuplot mctdhx_gnuplot plot 20 00000000rbs dat u 1 8 u 1 sqrt 24 2 u 1 sqrt 22 2 The plot command visualizes the density p x column 8 and the first two natural orbitals oN x and SX x column 24 and 22 respectively in the last ASCII output file of the relaxation 20 0000000o0rbs dat For
52. rely modular i e all subroutines are collected in Fortran modules To inspect the program structure please consult the html documentation by opening the index html file in the documentation htm1 subdirectory In this html documentation all important variables are explained and for each routine call and caller graphs are given 3 2 Analysis Program The analysis program can be run by typing MCTDHX_analysis The analysis program is serial i e no shared or distributed memory parallelization is used so far The program is also en tirely modular and the structure call and caller graphs as well as a documentation of impor tant variables is available in the same html documentation as for the main program see file documentation html index htm1 3 3 Scripts In the subdirectory Computation_Scripts there is the Monster sh script that can configure whole series of computations The input file ParameterScan inp is in the Input_Examples directory and contains an in line documentation Monster sh allows a scan of 5 user defined parameters for the relaxation and 5 user defined parameters for the subsequent propagations A parameter scan for potential DVR particle or orbital number and magnitude and or width of the interaction can be configured for instance The configuration of Monster sh is detailed in table 12 Furthermore Computation_Scripts contains the visualization master script vms sh that automatically runs the MCTDHX analysis p
53. results gt gt i Check results gt gt eae rere aber er Figure 7 The main tab of Guantum Here it is extended so as to display information on the status of an MCTDH X computation second column On the last column the video files can produced and reproduced 7 5 INPUT FILE DRIVEN USAGE MCTDH X Plots graphics and videos of the results 8 Last by clicking on Animate results you will see the section of the videos last column on the right Choose the type of video you wish to compile the plot range and the number of plot points and then click on Compile movies button Once compiled probably after few hours you will be able to choose the movie files created and watch them Click on Choose file to choose the desired video file and then play button and an mplayer window will pop up reproducing the created movie 5 Input File driven Usage MCTDH X The basic workflow of a numerical solution of the time dependent many boson Schrodinger equa tion H W i0 V TDSE with MCTDH X is the following 1 Define the Hamiltonian Modify Get_InterParticle_Potential F and Get_1bodyPotential F 2 Define the initial state W Modify Get_Initial_Coefficients F and Get_Initial_Orbitals F 3 Solve the TDSE by propagating in real or imaginary time libmake then libcp maybe inpcp modify MCTDHX inp finally MCTDHX 4 Analyze and visualize the solution maybe inpcp modify analysis inp
54. riable For each point in time t a line in this file contains the probability P t to find 2 particles to the left of border the probability P t to find one particle to the left and one to the right of border and the probability P t to find two particles to the right of border Column 1 to 4 Column 5 Column 6 Column 7 amp 8 Column 9 Mes Tiy P2051 2y pit et p pO rilat Table 28 The structure of the lt time gt N lt N gt M lt M gt lt x k gt lt Slice 1 gt lt Slice 2 gt correlations dat files These are output by the analysis program if the analysis input variable MOMSPACE2D or REALSPACE2D is set to T lt Slice 1 2 gt specify which cut through the real or momentum space density are in the file Column 1 and 2 Column 3 Column 4 and 5 Column 6 Column 7 Tis Tiy p ri t pPI lert pP rt Table 29 The structure of the lt time gt N lt N gt M lt M gt lt x k gt SkewCorrelations dat files These files are output of the analysis program if the analysis input variable MOMSKEW2D or REALSKEW2D is set to T Column 1 Column 4 Column 5 Column 6 M amp Column 8 M amp to3 to 5 M 7 M 9 M to 8 3M amp 9 3M T Y Z avg T Y z t x y z t V xEavg Z Y 25 t amp Vx81 Z y 25 t amp to Vols 24 Vii y z t to Em x y 2 t Vz m y 2 t amp Vy m z Y 7 t Table 30 The structure of the l
55. rogram and visualizes a given computation The g 4 GUANTUM THE MCTDH X GUI possible different visualization videos and plots are realized as bash scripts which can be found in the Visualization Scripts directory 4 Guantum using MCTDH X with a Graphical User In terface Guantum is a java graphical user interface GUI for the the Multiconfigurational Time Dependent Hartree method for Bosons or Fermions It is distributed together with the MCTDH X package Guantum is easy to handle and it requires no previous profound knowledge on many body quantum physics or programming skills As such it is aimed to be used by both advanced researchers on theory of ultracold bosons and fermions experimentalists as well as advanced students and researchers from other fields of physics or science On the Guantum window there are four clickable tabs On each of them you can define all the parameters that are required to start up an MCTDH X calculation as well as the external potential second tab that confines the system All input fields are self explained and have some default values except for the dimensions button If you are unsure about a setting it is recommended that you leave its default value unchanged or further study the present documentation 4 1 The tabs First Tab On the main first tab you see the buttons to choose the number of dimensions D the number of orbitals you wish to include in your MCTDH X calculation the number of p
56. ror message prompting you to first create and name your project You are strongly advised to first create your project and then submit a job Otherwise if you submit a job before creating a New project all files that are so far in the tmp directory will indeed be copied to the New_project directory but if the job is still running which is highly probable the newer results of the job will not be copied to the New_project directory and they will be lost once Guantum is exited 5 You can open a past project by clicking on File Open shortcut as usual Ctrl O In the 4 2 What Guantum Can Do 4 GUANTUM THE MCTDH X GUI file chooser you see a list of all project directories Choose the one you wish to open and then click on the gnm file with the same project name to facilitate the search the results on the file chooser are filtered so that you only see directories and gnm files When clicking on Open all saved values of the particular project are passed to Guantum 6 Once all the parameters have the desired values and you are ready to submit a job and you just click on the GO button of the first tab This saves the parameters values to both MCT DHX inp and ProjectName gnm files writes and executes the run script runscript sh In other words it submits your job to your local machine or the server Hassle free Checks how your calculation is doing 7 After you have submitted your job you can check its st
57. s 3 4 and 5 3 means full interaction matrix will be stored very large array 4 interac tion matrix evaluated with successive FFT IMEST 5 means time dependent interaction with IMEST 6 means time dependent contact interaction default 0 Table 5 MCTDH X main program input file parameters 25 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X Special parameters to treat multi level atoms and spinors In order to treat particles that have internal structure like multileveled atoms or spinor particles a set of special input variables has been introduced to the above System Parameters Namelist These define the number of levels the presence of a conical intersection and whether the interpar ticle interaction contains a spin dependent part or not In principle a conical intersection amounts to off diagonal terms in the one body Hamiltonian he which couple the different levels whereas a spin dependent interparticle interaction means that there is two particle interactions Wepin that can change the spin of particles These terms read as follows co 7 Vin 8 1z RODI WiFi ijk 3 Won gt S 81A WEF 75t S 81 4 V T y z Here the operator j was defined which makes level j appear in the coordinate space of level k for the spinor orbital on its right Furthermore the representation S was introduced for the general spin operators in v x y z direction Generally when t
58. s finished we can get a quick visual ization of the final state by typing mctdhx_status sh gnome open status png The script mctdhx_status sh plots the time evolution of the fragmentation in a computation as well as a snapshot of the current density The picture you should see is displayed in Figure Finally we could invoke several different bash scripts to visualize the computed time evolution as movies cf table or simply run all available scripts with the visualization master script like so vms sh all PWD 7 0 9 0 cf also section 5 3 vms sh automatically runs the analysis program on the data in the present di rectory and creates videos of the density as well as the correlation functions of the system For refer ence these are also available on the website at http ultracold org documentation 3 Program Structure The MCTDH X package contains a main program to perform the actual numerical task and an analysis program that is used to compute the desired quantities of analysis from the many body i 3 1 Main Program 3 PROGRAM STRUCTURE wavefunction For the purpose of visualization bash scripts that generate mpg or avi video files by running gnuplot and mencoder are provided A source tarball of gnuplot and mencoder are provided with MCTDH X in the External_Software subdirectory and installed with the installation script as mentioned above To automate and simplify the use of the main program the analysis program as
59. t Potential Namelist whichpot Select from predefined list of poten Character no default tials see table parameter Parameters to tune predefined poten Real default 1 0 parameter2 15 Parameters to tune predefined poten tials see table Real default 0 0 Interaction Namelist Which_Interaction Select predefined interparticle interac tion potentials Character default gauss For time dependent interac tions TDHIM TDgauss1 a Gaussian sinusoidially modulated amplitude and TDgauss2 a Gaussian with sinusoidially modulated width are currently defined Interaction_Width Modify parameter in the interparticle interaction Real default 0 15 24 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X interaction_parameter1 10 Parameters to tune predefined interac Real default 0 0 Interaction_Type tion potentials see table How the Local interaction potentials A W and their action is evaluated Integer 0 means like con tact interaction potential 1 to 4 will use the routine Get_InterParticlePot to generate the interaction potential 1 means the potential is separable and hence one potential vector is allocated for each spatial dimension 2 means the potential depends on the distance of the particles only hence a tridiagonal repre sentation is used only for aequidistant DVR
60. t kxfin2 Restricted grid stop Real no default kpts2 Number of grid points for restricted Integer no default grid lossops Loss operators i e projectors on Logical default F N 2 Hilbert space border Border partitioning N 2 Hilbert Real no default space for evaluation of the loss oper ators TWO_D MOMSPACE2D Output of 2D correlation functions Logical default F g r 7 and g 7 r1 in slices REALSPACE2D Output of 2D momentum correla Logical default F tion functions slices REALSKEW2D Output of 2D skew correlation func Logical default F tion gP F F t and gP 7 7 t MOMSKEW2D Output of 2D skew momentum cor Logical default F relation function g k k t and g k ka t xlconst Keep X coordinate of first position Logical default T momentum F k1 constant 31 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X xlslice At which value to keep the X Real default 0 0 coordinate of F k1 ylconst Keep Y coordinate of first position Logical default T momentum F k1 constant ylslice At which value to keep the Y Real default 0 0 coordinate of F k1 x2const Keep X coordinate of second posi Logical default F tion momentum 7 k constant x2slice At which value to keep the X Real default 0 0 coordinate of 7 k y2const Keep
61. t queueing systems prevent aliases from working and the executables then have to be copied and run in the current working directory MCTDHX_analysis executes the the analysis program for interactive use only Most queueing systems prevent aliases from working and the executables have to be copied and run in the current working directory libcp copy the dynamic library libmctdhx so to the current working directory inpcp copy the example inputs MCTDHX inp analysis inp to the current direc tory bincp copies the executables of the main and analysis programs to the current directory libmake will recompile the dynamic library libmctdhx so x make will recompile the whole program mctdhx_hg alias to the supplied mercurial distribution can be used for version man agement and to update the program mctdhx_gnuplot supplied gnuplot program to visualize data mctdhx_mencoder supplied mencoder program to make movies from gnuplot images mctdhx_mplayer supplied mplayer program to view the movies Table 2 Aliases and scripts provided with the MCTDH X installation aliases marked by a are only created if respective included software is not present in the system 2 An MCTDH X Tutorial A straightforward way of familiarizing youself with the usage of MCTDH X without further read ing the remainder of this user manual is to follow this step by step tutorial The tutorial includes
62. t time gt N lt N gt M lt M gt phase dat files The generation of the files is toggled by setting the analysis input variable PHASE to T If addi tionally GRADIENT it set to T then Columns 8 M to 9 3M containing the phase gradients will be generated Here x y z are the coordinates Eavg y z t is the average phase 2 y z t to E x y 2 t are the M orbital phases ViEaug x Y Z t amp VyEavg 2 Y z t is the x and y com ponent of the average phase s gradient and V 2 y z t amp Vy amp i x y z t to VrEu a y zt amp VyEu 2 y zt are the z and y components of the gradients of the M orbital phases 7 Developer Guidelines The MCTDH X program package uses Mercurial as a version management and provides a docu mentation in pdf format as well as a html code documentation generated by Doxygen Generally if you are planning to implement something useful it is recommended to browse the code documen tation in documentation html index html to find out in which module to start The package developers will also be happy to help you with this r 8 VERSION MANAGEMENT In writing code please stick to the following principles 1 2 3 8 write code that is readable use indentation and obvious variable and subroutine names write code that is modular group written subroutines or variable declarations into modules use CamelCase naming conventions where appropriate Every new word in declarations
63. te Name of input template in working di rectory usually MCTDHX inp for a single propagation computation Relaxtime Time to run relaxations for Positive number NParameters Number of parameters to scan for re 1 5 laxations Parameter 1 5 name of relaxation parameter Any parameter found in MCTDHX inp List 1 5 specifies if a list of values is T F used for relaxation parameter Parameter List 1 5 if List T specifies pa Array rameter values to scan over Scan Start 1 5 if if List F speficies be number ginning of range of relaxation parame ter to be scanned Scan Stop 1 5 if if List F speficies end number of range of relaxation parameter to be scanned Scan Step 1 5 if if List F speficies step number of range of relaxation parameter to be scanned MaxNodes Maximum number of nodes allocated Positive integer Prop_Time_Final End time of propagation computations Positive number Prop_NParameters Number of propagation parameters to scan over 1 5 Prop_Parameter 1 5 name of propagation parameter 4 Any parameter in MCT DHX inp Prop_List 1 5 specifies if a list of values is used for propagation paramter se F bj Prop_Parameter List 1 5 if Prop_List T speci fies propagation parameter values to scan over list of appropriate va
64. te non linear Schr dinger equation is possible Contrary to the approaches like time evolved block decimation matrix product states or time dependent density matrix renormalization group MCT P 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X DBH can provide accurate predictions in time and for higher dimension than D 1 because the partitioning of the Hilbert space is done by the variational principle and not artificially introduced The parameters to select the former exact diagonalization or the latter MCTDBH approach are collected in the following table System Parameters Namelist Parameter Meaning Options Bose_Hubbard Do an exact diagonalization of a Bose Hubbard Hamiltonian Atten tion Has to be used together with JOB_TYPE FCI Logical default F Periodic_BH Has the treated lattice system peri odic boundary conditions Logical default F DVR Parameters Namelist DVR_ lt I gt If DVR lt I gt 6 MCTDHB is ap plied to a lattice of that many sites in I X Y Z_ direction Atten tion has to be used together with JOB_TYPE BOS Integer default 4 It is important to note that in the case that an exact diagonalization of a Bose Hubbard Hamil tonian is done the one body potential offset is obtained from the routine Get_BH_Offset If MCTDHB applied to the Bose Hubbard Hamiltonian the default routine Get_1b
65. the external one body potential Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8 N of in Time t Execution Tstep Tor T TCI Fune Tord tegration time step Table 15 Timing dat file structure this table displays the column structure of the Timing dat output file Here Tstep is the execution time for the present integration step Tor Tp Tor runc iS the overall execution time in this step spent on the configuration interaction i e the coefficients part of the program T is the runtime consumed to invert the matrix elements of the reduced one body density Ter Func is the execution time consumed in applying the Hamiltonian to the coeffcients vector Tor finally is the execution time spent for evaluating the right hand side of the orbitals equations Column 1 to 3 Column 4 Column 5 Column 6 amp 7 Column 8 amp 9 Column 10 amp 11 to 10 2M amp 114 2M ei 2 DVR V a 9 2 1 Pult yY zt Pino lz Y zi t Ou 2 y 2b to weight pi z y z t Column 11 2M 1 amp 11 2M 2 to 11 4M 1 amp 11 4M 2 O a y zt to O g x y 2 t Table 16 lt time gt orbs dat file structure This table explains the column structure of the lt time gt orbs dat output files of the main or analysis program x y z are the spatial coordinates V x y z t is the one body potential p x y z t
66. the input variable Correlations X and Correlations K respectively are set to be true The files contain all nec essary quantities to compute the one body as well as the diagonal of the two body normalized pl x1 04 jt VJ plait p w st can be plotted as the value of Column 8 Column 9 divided by Column 7 x Column 10 Column 1 amp 2 Column 3 amp 4 Column 5 Column 6 zx ot kK pNarla st or p RIRs last ot pst oet or p t Glauber correlation function g and g respectively For instance g Table 26 Structure of the lt time gt N lt N gt M lt M gt lt x k gt corr lt 1 2 gt restr dat files The generation of these files is triggered by the analysis input variables corrirestr corr2restr corrirestrmom corr2restrmom Similar to the above table 25 the normalized correlation functions g and g can be computed from the contents of these files but for one dimensional computations and on a restricted grid which is specified through the analysis input variables lt x k gt ini lt 1 2 gt lt x k gt fin lt 1 2 gt lt x k gt pts lt 1 2 gt respectively r 7 DEVELOPER GUIDELINES Column 1 Column 2 Column 3 Column 4 Time t Pa PG POG Table 27 Structure of the lossops_N2_ lt border gt dat files The generation of such a file is triggered by the lossops input variable being set to T lt border gt is controlled by the border input va
67. time dependently modulated Fe h sin at lennart_j and 4 I Screened Lennart Jones W r r I m for r r gt Ip tential een and W 7 h a 4 for F 7 lt Ip HIM and 4 Harmonic interaction model W F 7 r 7 Table 4 Predefined time independent and time dependent interaction potentials Ix stands for Interaction ParameterX from the input o for Interaction Width and D for the dimensionality of the problem 5 2 Running the computation and analysis In this subsection it is specified how to run the MCTDH X program and analysis manually i e by configuring the MCTDHX inp and analysis inp input files and running the respective programs To read how to automate this process using the Monster sh and vms sh scripts please consult the next subsection The input of the main program To run the MCTDH X program it is best to have each calculation done in a separate direc r 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X tory The program needs two files to perform the computation First the dynamic library libmctdhx so and second the input file with computational numerical parameters MCTDHX inp The library contains the above four subroutines that define the Hamiltonian and the initial state Get_Initial_Coefficients F Get_Initial_Orbitals F Get_InterParticle_Potential F Get_1bodyPotential F If any of these files was modi
68. tum correla tion functions on the full grid Logical default F Geminals Toggle output of natural geminal oc Logical default F cupations in GO_PR out FullGeminals Toggle output of natural geminals in Logical default F lt time gt NzMy x geminals dat files 30 5 2 Running the computation and analysis 5 INPUT FILE DRIVEN USAGE MCTDH X corr lrestr Computation of spatial first order Logical default F correlation functions on a restricted grid xinil Restricted grid start Real no default xfinl Restricted grid stop Real no default xpts1 Number of grid points for restricted Integer no default grid corrlrestrmom Computation of spatial correlation Logical default F functions on a restricted momentum grid kxinil Restricted grid start Real no default kxfinl Restricted grid stop Real no default kpts1 Number of grid points for restricted Integer no default grid corr2restr Computation of spatial second order Logical default F correlation functions on a restricted grid xini2 Restricted grid start Real no default xfin2 Restricted grid stop Real no default xpts2 Number of grid points for restricted Integer no default grid corr2restrmom Computation of momentum second Logical default F order correlation functions on a re stricted grid kxini2 Restricted grid start Real no defaul
69. utine can also be selected and modified with the input parameters whichpot parameter1 parameter2 parameteri5 in MCTDHX inp or with the GUI respectively Table 3 collects the predefined potentials and parameters If a custom potential is desired it has to be implementated in the file source ini_guess_pot Get_1bodyPotential F look there for the loops which are enclosed by the if exceptions for whichpot eq custom1D custom2D custom3D respectively Specifying the two body potential W The two body interaction W is specified in the file Get_InterParticle_Potential F in the di rectory source ini_guess_pot This file contains a single Fortran subroutine with a case selec tion on the type of interparticle interaction and the evaluation of its action Interaction_Type is the corresponding input variable The standard types are a contact interaction potential Interaction Type 0 6 or short range Gaussian interaction Interaction Type 1 2 3 4 5 For these cases of a short range interparticle interaction the width of it can be adjusted with the input variable Interaction_Width in MCTDHX inp Generally a non contact interaction requires Interaction_Type gt 0 Interaction_type 5 is a time dependent non contact interaction and Interaction type 6 allows the simulation of contact interactions with a time dependent inter action strength The different evaluation types that Interaction Type selects and the necessary properties of the interaction
70. well this absence of fragmentation in the groundstate is anticipated There is however numerous examples on the emergence of fragmentation in the dynamics of ultracold bosonic systems To see the occurence of fragmentation it s therefore instructive to change the potential in which our eigenstate was computed and trigger some dynamics 2 2 Computing the Time Evolution of a System To propagate a given initial state in time one has to change only a few parameters in the MCTDHX inp file To start it s best to create a subdirectory for the propagation inside the MCTDH X Tutorial directory which contains the relaxation cd MCTDH X Tutorial mkdir propagation double well As indicated by the name we re going to propagate the groundstate of the harmonic potential which we computed in the previous subsection in a double well potential First we copy the necessary files to the newly created directory cp MCTDHX inp libmctdhx so analysis inp PSI_bin CIc_bin propagation double well cd propagation double well Subsequently the input file needs to be adapted with a text editor i e gedit MCTDHX inp To make the program propagate the initial state in the binary data files PSI_bin and CIc_bin the following parameters have to be adapted Job_Prefactor 0 d0 1 d0 GUESS BINR Binary_Start_Time 20 0d0 as also explained in the inlined documentation in the MCTDHX inp file and in table 5 Job_Prefactor 0 d0 1 d0 tr
71. well as the visualization bash scripts the program package also contains a graphical user interface Guantum as well as scripts that automate series of computations Monster sh and a script for the automation of data processing data_miner sh 3 1 Main Program The main program can be run by typing MCTDHX in wrappers or in runscripts the MCTDHX alias might not work and one needs to use MCTDHX_intel MCTDHX_pgf or MCTDHX_gcc Although in the case of a computationally intense task it is a lot faster to use the shared memory and distributed memory parallelization of the program and run it with one the various instances of MPI launchers such as mpirun mpiexec mpiexec hydra aprun Examples for running MCTDHxX in parallel can be found in the example PBS scripts directory PBS_Scripts Since the configuration of such an hybridly parallel job is complicated it is easier to just use the Monster sh script that will automate whole series of hybridly parallel computations They can be found in the Computation Scripts directory If a manual configuration of a task is needed or desired this is done by adapting one of the PBS runscript examples Depending on the hardware architecture the most efficient way is usually to run MCTDH X with at least as many MPI processes as there are orbitals The OpenMP shared memory parallelization takes care of efficiently performing the computational task inside of each MPI process The program s structure is enti
72. x exp x x tanh y Og C Leave unchecked if unsure Save Save Figure 6 Grid amp Interaction left as well as Advanced right tabs 3 and 4 of Guantum the graphical user interface of MCTDH X 3 To create a new project click on File New or use the keybord shortcut Ctrl N name the file on the popup window and click on Create Your project is created under path to mctdh x Guantum_Files ProjectName where lt ProjectName gt is the user defined name and the title now appears on the top of the window At the same time all the files created in the current unnamed session that are now in the tmp directory will be copied to the newly created directory with the chosen names 4 If you click on File gt Save or Ctrl S your selections and modifications are saved Simul taneously a Guantum file with the name lt ProjectName gt gnm is created This is a log file that stores all the input information so that it can be retrieved for future use Note that if you do not Save your project you will not be able to re open it For instance say you have started a calculation and have not created a New project yet but you then decide you want to keep the results The above process New Save will move all the existing files under your new directory and log all the information Note that you cannot commute these processes if you click on Save button before you have created a New project you will get an er

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