Numerical method for the stochastic projected Gross-Pitaevskii equation
| Autor: | P. B. Blakie, S. J. Rooney, Ashton S. Bradley |
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| Rok vydání: | 2014 |
| Předmět: |
Continuous-time stochastic process
Computer simulation Bose gas Numerical analysis Mathematical analysis FOS: Physical sciences Computational Physics (physics.comp-ph) Euler method Gross–Pitaevskii equation symbols.namesake Quantum Gases (cond-mat.quant-gas) Convergence (routing) symbols Applied mathematics Condensed Matter - Quantum Gases Representation (mathematics) Physics - Computational Physics Mathematics |
| Zdroj: | Physical Review E. 89 |
| ISSN: | 1550-2376 1539-3755 |
| DOI: | 10.1103/physreve.89.013302 |
| Popis: | We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional 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. 14 pages, 8 figures |
| Databáze: | OpenAIRE |
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