The stochastic Gross-Pitaevskii equation: II
The stochastic Gross-Pitaevskii equation: II
复制标题
DOI：
10.1088/0953-4075/36/23/010
复制
发表时间：
2003-12-14
影响因子：
1.6
通讯作者：
Davis, MJ
中科院分区：
文献类型：
--
作者：
Gardiner, CW;Davis, MJ
我们提供了随机Gross-Pitaevskii方程的更精确版本的推导，如由加德纳等人（2002 J. Phys. B：At.摩尔35 1555）。这种推导不依赖于局部能量和动量守恒的概念，而是基于玻色气体的“高温”主方程的准经典维格纳函数表示，其中仅包括能量截止ER以下的模式，这些模式被充分高度占据（冷凝带）。高于此截止值的模（非凝结带）被视为基本上是热化的。这两个带之间的相互作用，称为增长和散射过程，提供了噪声和阻尼项的运动方程的凝聚带，我们称之为随机格罗斯-Pitaevskii方程。这种方法的特点是在其推导中所作的近似控制和其数值实现的可行性。
We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 1555). This derivation does not rely on the concept of local energy and momentum conservation and is based on a quasiclassical Wigner function representation of a 'high temperature' master equation for a Bose gas, which includes only modes below an energy cut-off ER that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provides noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation and by the feasibility of its numerical implementation.