This function solves the gross pitaevskii equation in a twodimensional space. Gpelab, an open source matlab toolbox for the numerical. In preparation for the numerics we scale the 3d gross pitaevskii equation and obtain a fourparameter model. Computation of ground states of the grosspitaevskii.
Singularity formation and collapse in the attractive gross. Gpelab grosspitaevskii equation laboratory is a flexible matlab toolbox devoted to the numerical computation of stationary and. This paper presents gpelab grosspitaevskii equation laboratory, an advanced easytouse and flexible matlab toolbox for numerically simulating many. Numerical solution of the grosspitaevskii equation for. Effective josephson dynamics in resonantly driven bose. Gpelab is a free matlab toolbox for modeling and numerically solving large classes of systems of grosspitaevskii equations that arise in the physics of bose. Decay for travelling waves in the grosspitaevskii equation.
Bec is the minimization of the grosspitaevskii gp energy functional with. Gpelab1 grosspitaevskii equation laboratory is a flexible matlab toolbox devoted to the numerical computation of stationary and dynamical solutions of 1d 2d. In what follows, students will learn how to use the ndsolve command of mathematica. In this section the matlab code is presented that was used to solve the gpe. Grosspitaevskii functional, boseeinstein condensate, riemannian. The model equation that gpelab solves is the gross pitaevskii equation. Pdf gpelab, a matlab toolbox to solve grosspitaevskii. Gpelab, a matlab toolbox to solve grosspitaevskii equations ii. Comparing three numerical solvers of the gross pitaevskii equation posted on 03 february 2016.
Numerical solutions to the grosspitaevskii equation for bose. Computer physics computer physics communications 00 2014. The toolbox provides a variety of matlab classes for simulations based on the grosspitaevskii equation, the multiconfigurational. Pdf this paper presents gpelab grosspitaevskii equation laboratory, an advanced easytouse and flexible matlab toolbox for numerically simulating. 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. Comparing three numerical solvers of the grosspitaevskii. 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.
Abstract 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. Gsgpes is a matlab gnu octave suite of programs for the computation of the ground state of systems of grosspitaevskii equations. Nonlinear schrodinger equation multidimensional matlabbased. We study the numerical solution of the timedependent gross pitaevskii equation gpe describing a boseeinstein condensate bec at zero or very low temperature. Gsgpes is a matlabgnu octave suite of programs for the computation of the ground state of systems of grosspitaevskii equations.