Rényi熵的遍历平衡与随机虫洞
Ergodic Equilibration of Rényi Entropies and Replica Wormholes
摘要：
我们从多体量子系统汉密尔顿函数的高能谱中关于混沌的标准假设出发，研究了纯态的雷尼熵的行为。我们计算了雷尼熵的精确长时间平均值，并表明这些值周围的量子噪声在微正则熵中被指数抑制。对于微正则带上的离域态，长时间平均近似地再现了H. Liu和S. Vardhan，具有以非平面排列顺序产生的额外结构。我们分析了描述盒中平衡态黑洞的AdS/CFT系统的平衡态近似。我们将我们的分析推广到蒸发黑洞的情形，并对我们近似中新项的可能引力描述进行了评论。
英文摘要：
We study the behavior of Rényi entropies for pure states from standard assumptions about chaos in the high-energy spectrum of the Hamiltonian of a many-body quantum system. We compute the exact long-time averages of Rényi entropies and show that the quantum noise around these values is exponentially suppressed in the microcanonical entropy. For delocalized states over the microcanonical band, the long-time average approximately reproduces the equilibration proposal of H. Liu and S. Vardhan, with extra structure arising at the order of non-planar permutations. We analyze the equilibrium approximation for AdS/CFT systems describing black holes in equilibrium in a box. We extend our analysis to the situation of an evaporating black hole, and comment on the possible gravitational description of the new terms in our approximation.
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