发表机构
Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从通用哈密顿量出发，推导出探测粒子在热环境中的量子主方程、平衡条件及朗之万方程，揭示其随机动力学由底层场论对称性和尺度分离决定。
AI 中文摘要
从描述探测粒子与一组环境自由度相互作用的通用哈密顿量出发，我们推导了探测粒子约化密度矩阵演化的量子主方程、当环境处于热态时它们满足的一般平衡条件（该条件编码为实时间内延展的线算符的KMS性质），以及涌现出的朗之万描述。我们结果的新颖之处在于其普适性：我们不假设环境自耦合的具体形式、耦合粒子与环境的算符的具体形式、其关联函数的统计性质（无论动量转移的统计是高斯型还是非高斯型），也不假设探测粒子是否相对论性运动。我们的结果仅要求时空平移、宇称和时间反演是哈密顿量的对称性，并且探测粒子的色散关系特征尺度与环境特征尺度之间存在尺度分离。我们还讨论了高斯布朗运动涌现的极限情况。总体而言，我们的结果构成了对底层量子场论中哪些性质控制探测粒子能量损失和动量涨落的第一性原理推导。
英文摘要
Starting from a general Hamiltonian describing the quantum dynamics of probe particles interacting with a set of environment degrees of freedom, we derive the quantum master equation with which the reduced density matrix of a probe particle evolves, the general equilibration condition that they satisfy when the environment is prepared in a thermal state -- encoded in a KMS property for line operators extended in real time -- and the Langevin description that emerges. The novelty of our results resides in their generality: We do not assume a specific form of the environment self-coupling, of the environment operator that couples the particle to it, of the statistics of its correlation functions, whether the statistics of the momentum transfer is Gaussian or not, or whether the probe particles move relativistically. Our results only require that spacetime translations, parity and time reversal be symmetries of the Hamiltonian, and that there exists a separation of scales between those characterizing the dispersion relation of the probe particle and those of the environment. We also discuss the limiting case in which Gaussian Brownian motion emerges. Overall, our results constitute a first-principles derivation of what properties of the underlying quantum field theory govern the energy loss and momentum fluctuations of probe particles.
Comments44 pages
