2013/10/01 by S. J. Rooney, P. B. Blakie, Ashton S. Bradley +1 · 30 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Cold Atom Physics and Bose-Einstein Condensates #Consistency (knowledge bases) #Convergence (economics) #Geometry #Hermite polynomials #Mathematical analysis #Mathematics #Physics #Quantum Information and Cryptography #Quantum mechanics #Representation (politics) #Statistical physics #Strong Light-Matter Interactions #Thermalisation #cond-mat.quant-gas #physics.comp-ph
paper · pdf · doi:10.1103/physreve.89.013302
published in Physical Review E 89(1), 013302 (American Physical Society) · 14 pages, 8 figures
arxiv created 2013/10/01 · openalex publication_date 2014/01/10 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.