Hybrid phase-space simulation method for interacting Bose fields
Hybrid phase-space simulation method for interacting Bose fields
复制标题
相互作用玻色场的混合相空间模拟方法
DOI：
10.1103/physreva.78.013622
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发表时间：
2008
影响因子：
2.9
通讯作者：
P. Drummond
中科院分区：
文献类型：
--
作者：
S. Hoffmann;J. Corney;P. Drummond
我们引入一种近似相空间技术来模拟相互作用玻色子的量子动力学。未来的目标是处理玻色-爱因斯坦凝聚系统，该方法是为自然分离成高占用（凝聚）模式和轻占用模式的系统而设计的。该方法自一致地使用Wigner表示来处理高占用模式，使用正p表示来处理轻占用模式。在这种方法中，通常需要截断Fokker-Planck方程的高导数项。然而，至少在这里调查的案例中，在有限的时间内，产生的系统误差在较大的维格纳职业数的限制下消失。我们在两个相互作用的非谐波振荡器的系统上测试了该方法，分别具有高和低职业。混合方法成功地预测了原子正交，其模拟时间比正p方法长60倍。截断Wigner法在本试验中也表现良好。对于量子不拆测量方案的相关预测，对于同一系统，混合方法与精确结果吻合良好，而截断Wigner方法则存在较大的系统误差。
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.