论文标题
黑洞蒸发的随机统一电路模型
A Random Unitary Circuit Model for Black Hole Evaporation
论文作者
论文摘要
受黑洞蒸发的Hayden-Preskill协议的启发，我们考虑了量子多体Qudit系统的动力学，该系统耦合到外部环境，其中时间演化是由某些$ 2 $ loc的随机统一电路的连续限制驱动的。我们研究了两种情况，其中有或没有保守的$ U（1）$收费，并专注于动态的两个方面。首先，我们在分析和数值上研究系统的纠缠熵的生长，表明出现了两个不同的时间尺度：一个时间是内部动力学（争夺时间）的内在范围，而另一个则取决于系统 - 环境耦合。在存在$ u（1）$保守的电荷的情况下，我们表明纠缠遵循了类似页面的行为：它在“蒸发”的中间阶段开始减少，之后单调减少。其次，我们研究最初从环境测量中注入系统中最初注入系统中的信息所需的时间。基于明确的数值计算，我们在回避控制着初始配置是否控制时表征了此时间，这表明在两种情况下出现了不同的尺度。
Inspired by the Hayden-Preskill protocol for black hole evaporation, we consider the dynamics of a quantum many-body qudit system coupled to an external environment, where the time evolution is driven by the continuous limit of certain $2$-local random unitary circuits. We study both cases where the unitaries are chosen with and without a conserved $U(1)$ charge and focus on two aspects of the dynamics. First, we study analytically and numerically the growth of the entanglement entropy of the system, showing that two different time scales appear: one is intrinsic to the internal dynamics (the scrambling time), while the other depends on the system-environment coupling. In the presence of a $U(1)$ conserved charge, we show that the entanglement follows a Page-like behavior in time: it begins to decrease in the middle stage of the "evaporation", and decreases monotonically afterwards. Second, we study the time needed to retrieve information initially injected in the system from measurements on the environment qudits. Based on explicit numerical computations, we characterize such time both when the retriever has control over the initial configuration or not, showing that different scales appear in the two cases.
