Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas
Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas
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俘获玻色气体的耦合 Hartree-Fock-Bogoliubov 动力学方程
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
A. Griffin
中科院分区：
文献类型：
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作者：
Milena Imamovic;A. Griffin
利用Kadanoff-Baym非平衡格林函数形式，导出了捕获玻色凝聚气体凝聚波函数的自洽harree - fock - bogoliubov （HFB）无碰撞动力学方程和相关运动方程。我们的工作推广了凯恩和卡达诺夫关于均匀玻色气体的早期工作。我们包括了非对角线（异常）对相关性，因此除了正态（对角线）分布函数之外，我们还必须引入一个非对角线分布函数。这就得到了两个耦合的动力学方程。如果非对角线分布函数作为高阶贡献可以忽略不计，我们得到Zaremba， Griffin和Nikuni最近使用的半经典动力学方程（基于更简单的Popov近似）。讨论了耦合HFB动力学方程在半经典近似下的静态局部平衡解。我们还验证了一种解决方案是平衡冷凝水和非冷凝水密度曲线的刚性同相振荡，与陷阱频率振荡。
Using the Kadanoff-Baym nonequilibrium Green's-function formalism, we derive the self-consistent Hartree-Fock-Bogoliubov (HFB) collisionless kinetic equations and the associated equation of motion for the condensate wave function for a trapped Bose-condensed gas. Our work generalizes earlier work by Kane and Kadanoff for a uniform Bose gas. We include the off-diagonal (anomalous) pair correlations, and thus we have to introduce an off-diagonal distribution function in addition to the normal (diagonal) distribution function. This results in two coupled kinetic equations. If the off-diagonal distribution function can be neglected as a higher-order contribution, we obtain the semiclassical kinetic equation recently used by Zaremba, Griffin, and Nikuni (based on the simpler Popov approximation). We discuss the static local equilibrium solution of our coupled HFB kinetic equations within the semiclassical approximation. We also verify that a solution is the rigid in-phase oscillation of the equilibrium condensate and noncondensate density profiles, oscillating with the trap frequency.