论文标题
布朗SYK模型中的熵动力学注释
Note on entropy dynamics in the Brownian SYK model
论文作者
论文摘要
我们研究了Rényi熵的时间演变，该系统由两个耦合的Brownian Syk簇从初始产品状态演变而来。一个簇的Rényi熵线性生长，然后饱和到粗粒熵。此页面曲线是通过两种不同的方法获得的，一个路径积分鞍点分析和一个操作员动力学分析。使用动力学的布朗角色，我们得出了一个控制操作器动力学并为纯度提供页面曲线的主方程。对这个复杂的主方程的物理学的洞察力是通过补充路径积分方法提供的：分别负责Rényi熵的线性生长和饱和的副本和非对角线鞍。
We study the time evolution of Rényi entropy in a system of two coupled Brownian SYK clusters evolving from an initial product state. The Rényi entropy of one cluster grows linearly and then saturates to the coarse grained entropy. This Page curve is obtained by two different methods, a path integral saddle point analysis and an operator dynamics analysis. Using the Brownian character of the dynamics, we derive a master equation which controls the operator dynamics and gives the Page curve for purity. Insight into the physics of this complicated master equation is provided by a complementary path integral method: replica diagonal and non-diagonal saddles are responsible for the linear growth and saturation of Rényi entropy, respectively.
