Institut de Physique Théorique, CEA/DSM/IPhT-CNRS/URA 2306 CEA-Saclay, F-91191 Gif-sur-Yvette, France.
Phys Rev Lett. 2010 Dec 17;105(25):250401. doi: 10.1103/PhysRevLett.105.250401. Epub 2010 Dec 14.
We consider the question of thermalization for isolated quantum systems after a sudden parameter change, a so-called quantum quench. In particular, we investigate the prerequisites for thermalization, focusing on the statistical properties of the time-averaged density matrix and of the expectation values of observables in the final eigenstates. We find that eigenstates, which are rare compared to the typical ones sampled by the microcanonical distribution, are responsible for the absence of thermalization of some infinite integrable models and play an important role for some nonintegrable systems of finite size, such as the Bose-Hubbard model. We stress the importance of finite size effects for the thermalization of isolated quantum systems and discuss two scenarios for thermalization.
我们研究了在经历突然参数变化（所谓的量子淬火）后孤立量子系统热化的问题。特别是，我们研究了热化的前提条件，重点研究了时间平均密度矩阵的统计性质和最终本征态中可观测量的期望值。我们发现，与微正则分布采样的典型本征态相比，稀有本征态是某些无限可积模型热化缺失的原因，并对有限大小的某些非可积系统（如玻色-哈伯德模型）起着重要作用。我们强调了有限尺寸效应对孤立量子系统热化的重要性，并讨论了两种热化场景。
