bb_qdrop_hom

CODE STILL IN DEVELOPMENT

Overview

Solver of the density-unlocked extend Gross-Pitaevskii (GP) equations, for a homonuclear mixture, in three-dimensions (3D)

The code time steps using the Split-Step Fourier Method (SSFM), with both imaginary and real time. It relies on several libraries and packages:

• FFTW3 - A standard FFT library
• OpenMP - Shared memory parallelisation library
• HDF5 - Data format, used for outputting data here
• json-fortran - A JSON API for Fortran, used for input files for each simulation here

The code is structured as follows:

eqm.f03

The eqm program is the main program script of the code which loads in input data (see config.json) and calls other functions and subroutines for setting up grid, time-stepping, etc.

FFTW.f03

The FFTW module is simply to load FFTW into the code.

grid.f03

The grid module contains three functions for setting up the grids and differential operators:

1. space_grid(Nr,dr) - The spatial 1D grid arrays (Nr - the number of grid points, dr - the spatial step size)
2. mom_grid(Nr,dr) - The momentum space 1D grid arrays
3. exp_lap(kx,ky,kz,dt) -The Laplacian different operator written in the form exp(-0.5*dt*(kx^2 + ky^2 + kz^2)), as this is the form that is called within the SSFM time-stepping, so by defining this operator initially, there is a slight reduction in operations (kx, ky and kz are the three momentum space arrays, dt the time-step)

init.f03

The init module contains two functions for initialising the imaginary time-stepping:

1. init_wav(x,y,z,init_type,gauss_sig) - The initial wavefunction form (x, y and z are the three real space arrays, init_type allows for the selection of: a Gaussian initial density profile (init_type = 1); or a Super_Gaussian initial density profile (init_type = 2))
2. readin_wav(x,y,z,comp) - The initial wavefunction form loaded via an .h5 file, this can be loaded for both real and imaginary times (x, y and z are the three real space arrays, comp tells the function whether component 1 or 2 is being loaded)

time.f03

The time module contains two subroutines and one function for time-stepping the right-hand-side of the GP equation:

1. ssfm(psi1,psi2,dk2,t_steps,t_save,dt,dx,dy,dz,N1,N2,alpha,beta,eta,mu1,mu2,im_real) - The SSFM is employed here and can be used for both imaginary and real time (though the time-step dt must be defined to be real or imaginary before being passed to this subroutine). The main structure of this method is:

• Half potential step in real space
• Transform to Fourier space and compute the kinetic energy term
• Transform back to real space and compute the other half potential step
• Finally, additional calculations include chemical potential and renormalisation if in imaginary time This subroutine is also responsible for the in-time data outputting (to .h5 format), and for creating the FFTW plans (psi1 and psi2 are the wavefunctions, dk2 is the Laplacian operator in exponential form, t_steps number of time-steps, t_save number of steps between writing data, N1 and N2 are the rescaked atom numbers for the density-unlocked system, alpha, beta and eta are the three dimensionless parameters that define the equal mass density-unlocked mixture , mu1 and mu2 are the chemical potentials, and im_real denotes imaginary (im_real = 0) or real (im_real = 1) time)

2. renorm(psi,dx,dy,dz,N) - This subroutine renormalises the wavefunction (computed at each time-step in imaginary time)
3. chem_pot1(psi1,psi2,psi1_k,dk2,plan_back,Nx,Ny,Nz,dt,alpha,beta,eta) - The chemical potential of component-1 is calculated at each imaginary time-step, to aid in imaginary time convergence (psi1_k is the Fourier transform of wavefunction-1, and plan_back is the Inverse Fourier Transform plan)
4. chem_pot2(psi1,psi2,psi2_k,dk2,plan_back,Nx,Ny,Nz,dt,alpha,beta,eta) - The chemical potential of component-2 is calculated at each imaginary time-step, to aid in imaginary time convergence (psi2_k is the Fourier transform of wavefunction-2, and plan_back is the Inverse Fourier Transform plan)

rhs.f03

The rhs module contains two subroutines:

1. V_rhs1(psi1,psi2,mu1,alpha,beta,eta,dt,Nx,Ny,Nz) - The potential half-step (component 1).
2. V_rhs2(psi1,psi2,mu2,alpha,beta,eta,dt,Nx,Ny,Nz) - The potential half-step (component 2).
3. T_rhs(psi_k,dk2,Nx,Ny,Nz) - The kinetic energy step in momentum space.

Compiling and Running

Once the requisite libraries are loaded and located on the system, the next step is to setup up the config.json (the naming convention the code expects) file from the default.config.json file.

With the codes ready, the paths to the necessary libraries should be added to the associated Makefile (makefile_pc for local machines and makefile_hpc for remote clusters). Then copy the desired Makefile to makefile and run make to compile. If running locally then the code can be ran with the ./eqm command, whilst for running on a cluster, an example SLURM job script is given in either drop_eqm.sh or h5_eqm.sh:

• drop_eqm.sh - this creates a separate directory for the simulation data to be stored
• h5_eqm.sh - as above but sets up the reading in of the psi_init.h5 initial wavefunction file

Future...

Extension work will be undertaken on this code to include:

1. Processing scripts
2. Experimental to theoretical scripts to setup the config.json input file from experimental parameters