标题： 基于路径积分的两个耦合量子振子向准平衡态的弛豫 显示英文标题

标题： Relaxation of two coupled quantum oscillators to quasi-equilibrium states based on path integrals

摘要： 本文解决了开放量子系统松弛的问题。 使用路径积分方法，我们找到了两个耦合量子振子与不同振子浴相互作用的时间依赖密度矩阵的解析表达式。 密度矩阵的表达式是在所选振子之间的耦合常数的线性范围内得到的。 时间依赖的空间方差和协方差进行了分析和数值研究。 结果表明，尽管初始值不同，在长时间极限下的渐近方差总是符合涨落耗散定理。 在弱耦合方法中，有充分的理由相信子系统最终会各自处于平衡状态，即使整个系统内的温度差异任意。 显示英文摘要

摘要： The paper addresses the problem of relaxation of open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two coupled quantum oscillators interacting with different baths of oscillators. The expression for density matrix was found in the linear regime with respect to the coupling constant between selected oscillators. Time-dependent spatial variances and covariance were investigated analytically and numerically. It was shown that asymptotic variances in the long-time limit are always in accordance with the fluctuation dissipation theorem despite on their initial values. In the weak coupling approach there is good reason to believe that subsystems asymptotically in equilibrium at their own temperatures even despite of the arbitrary difference in temperatures within the whole system.