非马尔可夫浴的熵线性响应理论
Entropy Linear Response Theory with Non-Markovian Bath
摘要：
我们发展了一个微扰计算的熵动力学考虑系统和浴之间的突然耦合。我们所发展的理论可以在一般的环境下工作，而不需要马尔可夫近似。分别给出玻色子环境和费米子环境的微扰公式。我们发现Renyi熵响应只与系统和环境的谱函数以及特定的统计核分布函数有关。我们发现第二Renyi熵在短时间内是t^2增长/衰减，在长时间内是t线性增长/衰减。当环境温度较低时，费米系统Renyi熵的非单调行为是相当普遍的。当两个系统的温度接近时，得到了热输运的傅里叶定律。对Sachdev-Ye-Kitaev模型与自由费米子的耦合作了一致性检验，发现在一个与黑洞蒸发对偶的过程中存在一个类似Page曲线的动力学过程.发现在有能隙谱的环境中，纠缠熵存在振荡。
英文摘要：
We developed a perturbative calculation for entropy dynamics considering a sudden coupling between a system and a bath. The theory we developed can work in general environment without Markovian approximation. A perturbative formula is given for bosonic environment and fermionic environment, respectively. We find the Renyi entropy response is only related to the spectral functions of the system and the environment, together with a specific statistical kernel distribution function. We find a t^2 growth/decay in the short time limit and a t linear growth/decay in longer time scale for second Renyi entropy. A non-monotonic behavior of Renyi entropy for fermionic systems is found to be quite general when the environment's temperature is lower. A Fourier's law in heat transport is obtained when two systems' temperature are close to each other. A consistency check is made for Sachdev-Ye-Kitaev model coupling to free fermions, a Page curve alike dynamics is found in a process dual to black hole evaporation. An oscillation of entanglement entropy is found for a gapped spectrum of environment.
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