局部松弛中的层次递归
The hierarchy recurrences in local relaxation
摘要：
在一个经历幺正演化的封闭多体系统中，整个系统的一个小分区表现出局部弛豫。如果整个系统的总自由度是一个很大但有限的数，这样的局部松弛将遇到一个复发后，一定的时间，即局部系统的动力学突然出现随机后，良好的有序振荡衰减过程。本文发现，对于一个$N$二能级系统（TLS）的集合，其中一个TLS的局部松弛具有隐藏在递归后的随机性中的层次结构：相似的递归周期性地出现，并且后一个递归带来比前一个更强的随机性.我们得到的分析和数值结果很好地解释了这种层次递归：由于浴[剩余的$(N-1)$ TLS]的有限尺寸效应，局部TLS（作为一个开放系统）的种群周期性地扩散和重新聚集。我们还发现，所有$N$ TLS的熵之和即总关联熵近似呈现单调增加的趋势，而单个TLS的熵则呈现时增时减的趋势，整个$N$ -体系统的熵在幺正演化过程中保持不变.
英文摘要：
Inside a closed many-body system undergoing the unitary evolution, a small partition of the whole system exhibits a local relaxation. If the total degrees of freedom of the whole system is a large but finite number, such a local relaxation would come across a recurrence after a certain time, namely, the dynamics of the local system suddenly appear random after a well-ordered oscillatory decay process. It is found in this paper, for a collection of $N$ two-level systems (TLSs), the local relaxation of one TLS within has a hierarchy structure hiding in the randomness after such a recurrence: similar recurrences appear in a periodical way, and the later recurrence brings in stronger randomness than the previous one. Both analytical and numerical results that we obtained well explains such hierarchy recurrences: the population of the local TLS (as an open system) diffuses out and regathers back periodically due the finite-size effect of the bath [the remaining $(N-1)$ TLSs]. We also find that the total correlation entropy, which sums up the entropy of all the $N$ TLSs, approximately exhibit a monotonic increase; in contrast, the entropy of each single TLS increases and decreases from time to time, and the entropy of the whole $N$-body system keeps constant during the unitary evolution.
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