引力遍历性的提示：Berry的包围和半经典Page曲线的普适性
Hints of Gravitational Ergodicity: Berry's Ensemble and the Universality of the Semi-Classical Page Curve
摘要：
黑洞的最新进展表明，一个么正性相容的Page曲线可以从系综平均的半经典近似中得到。在本文中，我们强调（1）这种特殊的幺正性表现并不是黑洞所特有的，（2）它可以从一个基本的幺正理论的单一实现中出现。为了使事情更明确，我们考虑一个硬球气体从一个小盒子慢慢泄漏到一个更大的盒子。这是一个量子混沌系统，我们期望在完整的幺正描述中看到佩奇曲线，而半经典的本征态则期望表现得好像它们生活在贝里系综中。我们重现了这个系统的幺正兼容的页面曲线，半经典。该计算具有结构上的平行副本虫洞，关键依赖于合奏平均在每个时代，并揭示了多个时间尺度之间的相互作用的问题。使用系综平均$state$而不是纠缠熵，我们还可以设计一个信息“悖论”。我们的系统提供了一个具体的例子，其中的合奏的半经典佩奇曲线是一个遍历代理的时间平均，而不是一个明确的平均超过许多理论。我们在这里讨论的问题在逻辑上与视界的存在无关，所以我们期望半经典引力也应该以类似的眼光来看待。
英文摘要：
Recent developments on black holes have shown that a unitarity-compatible Page curve can be obtained from an ensemble-averaged semi-classical approximation. In this paper, we emphasize (1) that this peculiar manifestation of unitarity is not specific to black holes, and (2) that it can emerge from a single realization of an underlying unitary theory. To make things explicit, we consider a hard sphere gas leaking slowly from a small box into a bigger box. This is a quantum chaotic system in which we expect to see the Page curve in the full unitary description, while semi-classically, eigenstates are expected to behave as though they live in Berry's ensemble. We reproduce the unitarity-compatible Page curve of this system, semi-classically. The computation has structural parallels to replica wormholes, relies crucially on ensemble averaging at each epoch, and reveals the interplay between the multiple time-scales in the problem. Working with the ensemble averaged $state$ rather than the entanglement entropy, we can also engineer an information "paradox". Our system provides a concrete example in which the ensemble underlying the semi-classical Page curve is an ergodic proxy for a time average, and not an explicit average over many theories. The questions we address here are logically independent of the existence of horizons, so we expect that semi-classical gravity should also be viewed in a similar light.
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