标题： 非马尔可夫量子主方程和引力系统及引力退相干的福克-普朗克方程 显示英文标题

标题： Non-Markovian Quantum Master and Fokker-Planck Equation for Gravitational Systems and Gravitational Decoherence

摘要： 描述量子大质量系统与量子引力场相互作用的随机动力学的量子主方程，对于研究量子引力和量子信息问题，如引力的量子性质、引力诱导的纠缠和引力退相干是有用的。 电磁场导致量子系统退相干的研究表明，低温环境更有利于成功的量子信息处理实验。 同样，(微扰)引力的量子性质在低温下比高温下更容易显现，从而最小化热噪声的破坏性影响。 在这项工作中，我们推广了先前适用于高温情况的马尔可夫ABH主方程[1,2]的结果，推导出一个非马尔可夫量子主方程，用于约化密度矩阵，以及与之相关的福克-普朗克方程，用于两个质量遵循量子轨迹并与引力子场相互作用的随机动力学，包括引力子噪声的影响，适用于所有温度。 我们遵循影响泛函方法，如量子布朗运动的非马尔可夫胡-帕兹-张主方程[62,64]的推导所示。 我们发现，在低温极限下，约化密度矩阵的非对角元素随时间对数衰减，而温度相关部分则随时间二次衰减，这与马尔可夫情况明显不同。 我们以总结我们的发现和讨论作为结尾，说明这里研究的问题如何与[77]中为引力自力研究推导的量子随机方程相关，以及与量子光力学相关，因为在其中可以实现引力退相干和纠缠的实验观测。 显示英文摘要

摘要： A quantum master equation describing the stochastic dynamics of a quantum massive system interacting with a quantum gravitational field is useful for the investigation of quantum gravitational and quantum informational issues such as the quantum nature of gravity, gravity-induced entanglement and gravitational decoherence. Studies of the decoherence of quantum systems by an electromagnetic field shows that a lower temperature environment is more conducive to successful quantum information processing experiments. Likewise, the quantum nature of (perturbative) gravity is far better revealed at lower temperatures than high, minimizing the corruptive effects of thermal noise. In this work, generalizing earlier results of the Markovian ABH master equation [1,2] which is valid only for high temperatures, we derive a non-Markovian quantum master equation for the reduced density matrix, and the associated Fokker-Planck equation for the Wigner distribution function, for the stochastic dynamics of two masses following quantum trajectories, interacting with a graviton field, including the effects of graviton noise, valid for all temperatures. We follow the influence functional approach exemplified in the derivation of the non-Markovian Hu-Paz-Zhang master equation [62,64] for quantum Brownian motion. We find that in the low temperature limit, the off-diagonal elements of the reduced density matrix decrease in time logarithmically for the zero temperature part and quadratically in time for the temperature-dependent part, which is distinctly different from the Markovian case. We end with a summary of our findings and a discussion on how this problem studied here is related to the quantum stochastic equation derived in [77] for gravitational self force studies, and to quantum optomechanics where experimental observation of gravitational decoherence and entanglement may be implemented.