arXiv 1203.44582012-03-20cond-mat.quant-gas

玻色凝聚气体的时空相干性

Spatial and temporal coherence of a Bose-condensed gas

Yvan Castin, Alice Sinatra

备注：: 25 pages, 5 figures ; contribution to the Springer\&Verlag book "Quantum Fluids: hot-topics and new trends", edited by A. Bramati and M. Modugno

摘要：

本章的中心问题是三维空间均匀玻色凝聚气体的时间相干性，最初在有限温度下制备，然后演变为一个孤立的相互作用系统。第一个理论工具是一个数量守恒的Bogoliubov方法，允许描述系统作为一个弱相互作用的准粒子气体。这种方法自然地引入了凝聚态的相位算子：一个中心作用者，因为时间相干性的丧失是由凝聚态相变的扩散决定的。第二个工具是描述准粒子的Beliaev-Landau过程的动力学方程组。我们发现，在一般情况下，在长时间$t$的凝聚相变的方差是一个弹道项$\propto t^2$和扩散项$\propto t$的温度和相互作用相关的系数的总和。在热力学极限下，扩散系数与系统体积成反比。$t^2$的系数按体积平方的倒数乘以系统在初始状态下的能量的方差来缩放，并且也可以通过量子遍历理论（所谓的本征态热化假设）来获得。

英文摘要：

The central problem of this chapter is temporal coherence of a three-dimensional spatially homogeneous Bose-condensed gas, initially prepared at finite temperature and then evolving as an isolated interacting system. A first theoretical tool is a number-conserving Bogoliubov approach that allows to describe the system as a weakly interacting gas of quasi-particles. This approach naturally introduces the phase operator of the condensate: a central actor since loss of temporal coherence is governed by the spreading of the condensate phase-change. A second tool is the set of kinetic equations describing the Beliaev-Landau processes for the quasi-particles. We find that in general the variance of the condensate phase-change at long times $t$ is the sum of a ballistic term $\propto t^2$ and a diffusive term $\propto t$ with temperature and interaction dependent coefficients. In the thermodynamic limit, the diffusion coefficient scales as the inverse of the system volume. The coefficient of $t^2$ scales as the inverse volume squared times the variance of the energy of the system in the initial state and can also be obtained by a quantum ergodic theory (the so-called eigenstate thermalisation hypothesis).

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