Gpelab, an open source matlab toolbox for the numerical simulation of gross pitaevskii equations. It allows for simulation of n level quantum systems, bosehubbard type systems and boseeinstein condensates described by the onedimensional grosspitaevskii equation. It is similar in form to the ginzburglandau equation and is sometimes referred to as a nonlinear schrodinger equation. The grosspitaevskii equation is a nonlinear model equation for the order parameter or wavefunction of a boseeinstein condensate. The following program is an example of how the user. We investigate the 1d generalized gross pitaevskii equation ggpe with quadratic potential and parameterized nonlinearity. It can compute the ground state in the defocusing case, for any number of equations with harmonic or quasiharmonic trapping potentials, in spatial dimension one, two or. May 18, 2004 i am thinking of solving a nonlinear equation, namely, gross pitaevskii equation that applied in bose einstein condensates. Gpelab, a matlab toolbox to solve gross pitaevskii equations i. Gpue is a grosspitaevskii equation solver that is accelerated on gpu hardware. Solving the gpe lets us describe a dilute becs ground state as well as its linear and nonlinear excitations and.
Follow 282 views last 30 days andrew on 28 oct 2014. Gpue is a fast, robust, and accessible software suite to simulate physics for fundamental research in the area of. Matlab is a mathematical computational software program. Solving the gpe lets us describe a dilute becs ground state as well as its linear and nonlinear excitations and transport properties at ultralow temperatures. The coefficients of terms of ggpe studied are arbitrary functions of time t. Gsgpes is a matlab gnu octave suite of programs for the computation of the ground state of systems of grosspitaevskii equations. Solver for the twodimensional grosspitaevskii equation.
Dynamics and stochastic simulations xavier antoine, romain duboscq computer physics communications. I wrote a code to solve the grosspitaevskii equation on a sphere which i solved analytically with the lagrange multipliers. I was hoping someone might be able to give a approachable explanation of the gross pitaevskii equation. Qengine is our software library for quantum simulation and optimization. The grosspitaevskii energy for the rotating condensate we consider in this paper numerical methods for the direct minimization of the grosspitaevskii energy. The problem is boundary and initial conditions that i cant find a way to determin. This code defines an existing function and step size which you can change as per requirement. The grosspitaevskii equation describes the properties of a dilute. I am trying to solve the grosspitaevskii equation numerically and using ndsolve, but this seems to be a dead end. A timesplitting pseudospectral method for the solution of. This software is a cudaenabled nonlinear schrodinger gross pitaevskii equation solver. The model equation that gpelab solves is the grosspitaevskii equation.
Since the nlse is nonlinear, many of the most interesting dynamical solutions do not have a closed form and require the use of direct numerical simulations. I am trying to solve the gross pitaevskii equation numerically and using ndsolve, but this seems to be a dead end. Quantum turbulence simulations using the grosspitaevskii. This paper is concerned with the numerical investigation of quantum turbulence qt described by the gross pitaevskii gp equation. Langmuir dependence of bicellar system phase behavior and dynamics on anionic lipid concentration. A linear systemfree gaussian rbf method for the grosspitaevskii equation on unbounded domains. Gsgpes is a matlabgnu octave suite of programs for the computation of the ground state of systems of grosspitaevskii equations. Lev pitaevskii started collaborating with the university of trento at the end of the 1980s through a series of long term visits. Gpelab is a free matlab toolbox for modeling and numerically solving large classes of systems of grosspitaevskii equations that arise in the physics of boseeinstein condensates. Pdf gpelab, a matlab toolbox to solve grosspitaevskii. Referenced in 24 articles fortran programs for the timedependent gross pitaevskii equation in a fully anisotropic trap. Journal of mathematics a unified software framework for empirical gramians. It can compute the ground state in the defocusing case, for any.
All the sources ive been able to find seem to concentrate on the derivation, and i dont have the physics background to follow. Jan 16, 20 this code defines an existing function and step size which you can change as per requirement. It allows for simulation of n level quantum systems, bosehubbard type systems and boseeinstein condensates described by. Exact soliton solutions of the 1d generalized gross.
The toolbox provides a variety of matlab classes for simulations based on the gross pitaevskii equation, the multicon gurational hartree method for bosons, and on generic fewmode models, as well as optimization problems. Fortran programs for the timedependent grosspitaevskii equation in a fully. My name is elias and ive been working with xmds2 for about 6 months now. Numerical solutions to the grosspitaevskii equation for boseeinstein condensates by luigi galati b. This paper is concerned with the numerical investigation of quantum turbulence qt described by the grosspitaevskii gp equation. We begin with the threedimensional 3d grosspitaevskii equation gpe with an angular momentum rotation term andor longrange ddi, state the twodimensional 2d gpe. Solver for the twodimensional gross pitaevskii equation. Based on your location, we recommend that you select. Octbec a matlab toolbox for optimal quantum control of bose. Grosspitaevskii equation in boseeinstein condensates. Gpelab, a matlab toolbox to solve grosspitaevskii equations. Gpue is gpu accelerated software to solve the grosspitaevskii equation for. Matlab including builtin visualization and analysis tools.
This talk presents gpelab grosspitaevskii equation laboratory, an advanced easytouse and flexible matlab toolbox for numerically simulating many complex physics situations related to boseeinstein condensation bec. Follow 95 views last 30 days freestyler000218 on 28 mar 2012. Gpelab is a free matlab toolbox for modeling and numerically solving large classes of systems of gross pitaevskii equations that arise in the physics of boseeinstein condensates. This paper presents gpelab grosspitaevskii equation laboratory, an advanced easytouse and flexible matlab toolbox for numerically simulating many complex physics situations related to boseeinstein condensation. Sarra, the matlab radial basis function toolbox, journal of open research software, march 27, 2017. Weakly nonlinear analysis of vortex formation in a dissipative variant of the grosspitaevskii equation. Gpelab 1 g ross p itaevskii e quation lab oratory is an open access matlab toolbox developed for computing the stationary states and the nonlinear deterministic and stochastic dynamics of 1d2d3d gross pitaevskii equations gpes. This function solves the grosspitaevskii equation in a twodimensional space. Gsgpes is a matlab gnu octave suite of programs for the computation of the ground state of systems of gross pitaevskii equations. Trial software how to do runge kutta 4 with a second order ode. Sometimes i find some difficulties and now its one of them. Automatic differentiation in matlab using admat with. The primary use of this code was for my research on rapidly rotating boseeinstein condensates. The main application is the computation of di erent types of vortex states abrikosov vortex lattice, giant vortex in rotating boseeinstein condensates.
Gpelab is a matlab toolbox developed to help physicists for computing ground states or dynamics of quantum systems modeled by grosspitaevskii equations. Pdf computational methods for the dynamics of the nonlinear. It contains various physical models, including twoparticle, bosehubbard, and gross pitaevskii. Ed, university of florida a thesis submitted to the graduate faculty of georgia southern university in partial ful llment of the requirement for the degree master of science statesboro. Robust and accurate numerical schemes are implemented for computing. Although matlab has builtin vectorized computations, the script codes still run slow compared to compiled c or fortran codes for many applications. Matlab postprocessing suite removal of gibbs oscillations from the chebyshev and fourier approximation of discontinuous functions. The toolbox provides a variety of matlab classes for simulations based on the grosspitaevskii equation, the multicon gurational hartree method for bosons, and on generic fewmode models, as well as optimization problems. Gpelab a matlab toolbox for computing stationary solutions and. After a few years spent at the israel institute of technology in haifa he eventually became professor of trento university in 1998. Gpelab1 grosspitaevskii equation laboratory is a flexible matlab toolbox devoted to the numerical. Grosspitaevskii equation gpe determines the quantum wave function of a gas of bosons in the limit in which thermal and quantum fluctuations are negligibly small. A simple and efficient numerical method for computing the.
Runge kutta 4th order ode file exchange matlab central. These classes can be easily combined, which has the advantage that one can adapt the simulation programs. Computing stationary solutions for a class of systems multicomponents of grosspitaevskii equations in 1d, 2d and 3d. Gpue is a gpubased grosspitaevskii equation solver via the splitoperator method for superfluid simulations of both linear and nonlinear schrodinger equations, emphasizing superfluid vortex dynamics in two and three dimensions. It may be exploited to simulate the evolution of boseeinstein condensate in a static external potential, or to calculate the groundstate using the imaginary time evolution. Learn more about laplacian modified, second derivative, d, del2, diff matlab. Due to the complexity and timescales needed to simulate such system, it was essential to write some accelerated code to understand the behaviour of such systems. Im working with boseeinstein condensates and running a 2d single component grosspitaevskii equation solver for the simulations in matlab. Gpelab 1 g ross p itaevskii e quation lab oratory is an open access matlab toolbox developed for computing the stationary states and the nonlinear deterministic and stochastic dynamics of 1d2d3d grosspitaevskii equations gpes. Welcome to gpue, the fastest zero temperature bec routines in the land the last time we checked. This software is a cudaenabled nonlinear schrodinger grosspitaevskii equation solver. We propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating boseeinstein condensates becs in a rotational frame with or without longrange dipoledipole interaction ddi. The exact solutions of the ggpe are obtained via expansion method with particular soliton features highlighted.
Gpelab, a matlab toolbox to solve gross pitaevskii equations ii. There is a way to achieve e cient largescale codes in matlab which is is to write custom c codes which connect to matlab through an interface compiler called mex. We investigate the 1d generalized grosspitaevskii equation ggpe with quadratic potential and parameterized nonlinearity. Gpelab a free matlab toolbox to compute and simulate bose. An open source virtual laboratory for the schrodinger equation. The current first version of the qengine allows for simulation of the onedimensional schrodinger equation for single and two particle systems. Software, environments and tools automatic differentiation in matlab using admat with applications 10.
Currently, there are standard software packages like gpelab in matlab or. This function solves the gross pitaevskii equation in a twodimensional space. Abstract abstract gpelab is a free matlab toolbox for modeling and numerically solving large classes of systems of gross pitaevskii equations that arise in the physics of boseeinstein condensates. Graphics processing unit grosspitaevskii equation solver. The software computes 2d or 3d stationary solutions of the gross pitaevskii equation with rotation. Oct 19, 2019 gsgpes is a matlabgnu octave suite of programs for the computation of the ground state of systems of grosspitaevskii equations. Numerical solutions to the gross pitaevskii equation for boseeinstein condensates by luigi galati b. Gpelab, a matlab toolbox to solve grosspitaevskii equations ii. Padua2dm a matlaboctave code for interpolation and cubature at the padua points, download code, references cdmsv09. The software computes 2d or 3d stationary solutions of the grosspitaevskii equation with rotation. Gpelab, an open source matlab toolbox for the numerical.
Gpelab grosspitaevskii equation laboratory is a matlab toolbox devoted to. Gsgpe, ground state for systems of coupled grosspitaevskii equations, download code, references cort09. Octbec a matlab toolbox for optimal quantum control of. Numerical simulations are performed using a parallel mpiopenmp code based on a pseudospectral spatial discretization and second order splitting for the time integration. How can solve laplacian of a function with coefficients. Balancing accuracy and energy of the control action, chaos. It can compute the ground state in the defocusing case, for any number of equations with harmonic or quasiharmonic trapping potentials, in spatial dimension one, two or three. The model equation that gpelab solves is the grosspitaevskii equation gpe. Gpelab, an open source matlab toolbox for the numerical simulation of grosspitaevskii equations. A quantum system created with qengine can be optimized out the box with several stateoftheart optimization algorithms. The way it works is that it numerically solves the gp equation and the end result leaves me with the ground state wave function of the bec in the harmonic trap, after which i do real time evaluation of the gp equation. This code has no new feature compared to existing codes available online.
The primary use of this code was for research on boseeinstein condensates. I was hoping someone might be able to give a approachable explanation of the grosspitaevskii equation. Choose a web site to get translated content where available and see local events and offers. This paper presents gpelab gross pitaevskii equation laboratory, an advanced easytouse and flexible matlab toolbox for numerically simulating many complex physics situations related to boseeinstein condensation. I am thinking of solving a nonlinear equation, namely, gross pitaevskii equation that applied in bose einstein condensates. The exact solutions of the ggpe are obtained via expansion method. Gpelab, a matlab toolbox to solve grosspitaevskii equations i. How to do runge kutta 4 with a second order ode learn more about runge kutta, second order ode. Referenced in 24 articles fortran programs for the timedependent grosspitaevskii equation in a fully anisotropic trap. The model equation that gpelab solves is the gross pitaevskii equation.
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