标题： 黑洞相变的非马尔可夫动力学 显示英文标题

标题： Non-Markovian dynamics of black hole phase transition

摘要： 我们基于底层自由能景观，对黑洞相变的非马尔可夫动力学进行了全面研究。 通过假设不同黑洞态之间的转变过程是随机的，黑洞相变的非马尔可夫动力学由广义朗之万方程描述，其中时间依赖的摩擦项表示当系统的时间尺度与有效热浴的时间尺度相当或更短时的记忆效应。 我们考虑与黑洞相变相关的首次通过问题，并推导了在弱摩擦、中间摩擦和强摩擦区域中平均首次通过时间的解析表达式。 作为具体的例子，我们研究了三种时间依赖的摩擦核（δ函数摩擦、指数衰减摩擦和振荡摩擦）对霍金-佩奇相变以及小/大RNAdS黑洞相变动力学的影响。 我们发现，当摩擦强度变化时，每种类型的摩擦核都存在一个动力学转折点。 对于指数衰减的摩擦核，结果表明在弱摩擦区域，非马尔可夫效应会减缓相变动力学，在强摩擦区域则会加快转变过程。 对于振荡衰减的摩擦核，我们发现当有效热浴的振荡频率等于自由能景观上初始势阱中黑洞态的振荡频率时，会出现动力学共振。 显示英文摘要

摘要： We provide a comprehensive study on the non-Markovian dynamics of the black hole phase transitions based on the underlying free energy landscape. By assuming that the transition processes between different black hole states are stochastic, the non-Markovian dynamics of the black hole phase transition is governed by the generalized Langevin equation with the time-dependent friction that represents the memory effect from the effective thermal bath when the timescale of the system is comparable or shorter than the timescale of the effective thermal bath. We consider the first passage problem associated with the black hole phase transitions and derive the analytical expressions of the mean first passage time in the weak, intermediate, and large friction regimes. As the concrete examples, we study the effects of three types of time dependent friction kernel (delta function friction, exponentially decayed friction, and oscillatory friction) on the dynamics of Hawking-Page phase transition and the small/large RNAdS black hole phase transition. we found that there is a kinetic turnover point for each type of friction kernel when the friction strength varies. For the exponentially decayed friction kernel, it is shown that the non-Markovian effect slows down the phase transition dynamics in the weak friction regime and speeds up the transition process in the strong friction regime. For the oscillating decayed friction kernel, we found kinetic resonances when the oscillating frequency of the effective thermal bath is equal to the oscillating frequency of the black hole state in the initial potential well on the free energy landscape.