标题： 量子混沌中的页曲线动力学机制 显示英文标题

标题： A dynamical mechanism for the Page curve from quantum chaos

摘要： 如果由纯态形成的黑洞的蒸发是幺正的，霍金辐射的纠缠熵应遵循Page曲线，从零开始增加，直到蒸发的中间点附近，然后又减少到零。Page曲线的一般论点基于这样一个假设，即黑洞加上辐射在蒸发过程中的量子态是典型的。在本文中，我们表明，Page曲线可以从黑洞演化的简单动力学输入中得出，这是基于最近提出的量子混沌的特征，而无需依赖典型性。我们的论点基于我们所谓的“算符气体”方法，该方法允许通过算符的海森堡演化的一般特征来理解黑洞微观态的演化。导致Page曲线的一个关键特性是“气体”中的算符可以“跳跃”出黑洞的可能性，我们将其称为虚空形成过程。这些过程最初被指数抑制，但在一定时间尺度后占主导地位，这可以作为Page时间的动力学定义。在年轻和老年黑洞的Hayden-Preskill协议中，我们证明虚空形成也负责将信息从黑洞传递到辐射中。我们猜想，虚空形成可能为最近半经典公式中在计算辐射纠缠熵时包括岛屿提供了一种微观解释。 显示英文摘要

摘要： If the evaporation of a black hole formed from a pure state is unitary, the entanglement entropy of the Hawking radiation should follow the Page curve, increasing from zero until near the halfway point of the evaporation, and then decreasing back to zero. The general argument for the Page curve is based on the assumption that the quantum state of the black hole plus radiation during the evaporation process is typical. In this paper, we show that the Page curve can result from a simple dynamical input in the evolution of the black hole, based on a recently proposed signature of quantum chaos, without resorting to typicality. Our argument is based on what we refer to as the "operator gas" approach, which allows one to understand the evolution of the microstate of the black hole from generic features of the Heisenberg evolution of operators. One key feature which leads to the Page curve is the possibility of dynamical processes where operators in the "gas" can "jump" outside the black hole, which we refer to as void formation processes. Such processes are initially exponentially suppressed, but dominate after a certain time scale, which can be used as a dynamical definition of the Page time. In the Hayden-Preskill protocol for young and old black holes, we show that void formation is also responsible for the transfer of information from the black hole to the radiation. We conjecture that void formation may provide a microscopic explanation for the recent semi-classical prescription of including islands in the calculation of the entanglement entropy of the radiation.