Typicality versus thermality: an analytic distinction
Typicality versus thermality: an analytic distinction
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典型性与热性：分析区别
DOI：
10.1007/s10714-008-0606-8
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发表时间：
2007
影响因子：
2.8
通讯作者：
J. Simón
中科院分区：
文献类型：
--
作者：
V. Balasubramanian;B. Czech;V. Hubeny;K. Larjo;Mukund Rangamani;J. Simón
在具有大简并态的系统中，如黑洞，人们期望探测相关函数的平均值将很好地近似于热系综。为了理解个体微观态中的相关函数与正则系综平均值以及彼此之间的差异，我们研究了量子数的方差。使用一般的统计考虑，我们表明，微观状态之间的方差将指数抑制的熵。然而，通过利用相关函数的分析性质，我们认为，这些方差在虚时间放大，从而区分纯态的热密度矩阵。我们证明了我们的一般结果在具体的例子，并认为我们的结果适用于黑洞的微观状态。
In systems with a large degeneracy of states such as black holes, one expects that the average value of probe correlation functions will be well approximated by the thermal ensemble. To understand how correlation functions in individual microstates differ from the canonical ensemble average and from each other, we study the variances in correlators. Using general statistical considerations, we show that the variance between microstates will be exponentially suppressed in the entropy. However, by exploiting the analytic properties of correlation functions we argue that these variances are amplified in imaginary time, thereby distinguishing pure states from the thermal density matrix. We demonstrate our general results in specific examples and argue that our results apply to the microstates of black holes.