Numerical method for the stochastic projected Gross-Pitaevskii equation

S. J. Rooney, P. B. Blakie, and A. S. Bradley
Phys. Rev. E 89, 013302 – Published 10 January 2014

Abstract

We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional weakly interacting Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes in the low-energy classical region of the system, and evaluating terms from the number-conserving scattering reservoir process. We give an accurate and efficient procedure for evaluating the scattering terms using a Hermite-polynomial based spectral-Galerkin representation, which allows us to precisely implement the low-energy mode restriction. Stochastic integration is performed using the weak semi-implicit Euler method. We extensively characterize the accuracy of our method, finding a faster-than-expected rate of stochastic convergence. Physical consistency of the algorithm is demonstrated by considering thermalization of initially random states.

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  • Received 1 October 2013
  • Revised 19 November 2013

DOI:https://doi.org/10.1103/PhysRevE.89.013302

©2014 American Physical Society

Authors & Affiliations

S. J. Rooney, P. B. Blakie, and A. S. Bradley

  • Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin, New Zealand

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Vol. 89, Iss. 1 — January 2014

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