Institute for Scientific Interchange, Torino, Italy.
Phys Rev Lett. 2011 Jul 1;107(1):010403. doi: 10.1103/PhysRevLett.107.010403.
The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this Letter we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasicritical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.
封闭量子系统的平衡动力学被编码在一般可观测量的长时间分布函数中。在这封信中，我们考虑了有限温度下的洛施密特回波，并表明我们可以为通过突然淬火描述的量子 XY 链得到其长时间分布的精确表达式。在热力学极限下，洛施密特回波的对数呈正态分布，而在相反的准临界区域中，对于小的淬火，分布函数呈现出通用的双峰形式，表明平衡不良。这些发现是通过中心极限定理类型的结果得出的，它们在小淬火区域扩展到完全一般的模型。
