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- Hybrid phase-space simulation method for interacting Bose fields
- Hoffmann, Scott E.; Corney, Joel F.; Drummond, P. D.
- We introduce an approximate phase-space technique to simulate the quantum dynamics of interacting bosons. With the future goal of treating Bose-Einstein condensate systems, the method is designed for systems with a natural separation into highly occupied (condensed) modes and lightly occupied modes. The method self-consistently uses the Wigner representation to treat highly occupied modes and the positive- P representation for lightly occupied modes. In this method, truncation of higher-derivative terms from the Fokker-Planck equation is usually necessary. However, at least in the cases investigated here, the resulting systematic error, over a finite time, vanishes in the limit of large Wigner occupation numbers. We tested the method on a system of two interacting anharmonic oscillators, with high and low occupations, respectively. The hybrid method successfully predicted atomic quadratures to a useful simulation time 60 times longer than that of the positive- P method. The truncated Wigner method also performed well in this test. For the prediction of the correlation in a quantum nondemolition measurement scheme, for this same system, the hybrid method gave excellent agreement with the exact result, while the truncated Wigner method showed a large systematic error.
- Publication type
- Journal article
- Physical Review A, Vol. 78, no. 1 (2008), article no. 013622
- Publication year
- FOR Code(s)
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics; 0204 Condensed Matter Physics; 0205 Optical Physics
- Anharmonic oscillators; BEC; Bose-Einstein Condensate; Difference equations; Finite time; Fokker Planck equation; Forecasting; FPE; Hybrid methods; Hybrid sensors; Industrial economics; Interacting bosons; Phase space methods; Phase spaces; QND; Quantum dynamics; Quantum nondemolition measurement; Quantum theory; Separation; Simulation time; Steam condensers; Systematic; Systems engineering; Turbulent flow; Wigner representation
- American Physical Society
- Publisher URL
- Copyright © 2008 The American Physical Society. Published version of this paper reproduced here in accordance with the copyright policy of the publisher.
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- Peer reviewed