|Title||Note on entropy dynamics in the Brownian SYK model|
|Publication Type||Journal Article|
|Year of Publication||2021|
|Authors||S-K. Jian, and B. Swingle|
|Journal||J. High Energy Phys.|
|Keywords||AdS-CFT Correspondence, Black Holes, Nonperturbative Effects, Random Systems|
We study the time evolution of Renyi entropy in a system of two coupled Brownian SYK clusters evolving from an initial product state. The Renyi 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 Renyi entropy, respectively.