Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation
Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation
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DOI：
10.1088/0953-4075/38/23/008
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发表时间：
2005-12-14
影响因子：
1.6
通讯作者：
Gardiner, CW
中科院分区：
文献类型：
--
作者：
Bradley, AS;Blakie, PB;Gardiner, CW
我们给出了描述囚禁玻色气体的高温随机Gross-Pitaevskii方程的Ehrenfest关系，其中包括生长噪声和能量截断的影响。发现了在Ehrenfest关系中忽略截止项的条件，该条件比通常的截断Wigner方法或经典场法的有效性条件--所有模都被高度占据--更为严格。该条件要求非线性相互作用项与非凝聚带的最低能量单粒子态有很小的重叠，并提供了一种在数值模拟中限制由于能量截止而引起的动力学伪影的方法。我们将这种形式应用于两个简单的测试问题：(I)模拟零温度下囚禁玻色气体的Kohn模振荡；(Ii)在经典场方法中计算有限温度玻色气体的平衡性质。这些例子表明了控制截止效应的方法，并且对于给定的截止能量，存在一个最佳的平面波基选择。这个基础给出了单粒子光谱、凝聚态分数、位置密度和动量密度的最佳再现。
We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.