标题： 耦合谐波系统的量子平均力吉布斯态结构 显示英文标题

标题： Structure of Quantum Mean Force Gibbs States for Coupled Harmonic Systems

摘要： 一个与给定温度的热浴相互作用的开放量子系统预期会达到平均力吉布斯（MFG）态作为稳态。 MFG态是通过从总系统加热浴的平衡吉布斯态中追踪出热浴自由度得到的。 当系统与热浴之间的相互作用不可忽略时，它不同于仅从系统哈密顿量得到的通常系统吉布斯态。 使用路径积分方法，我们给出了与多个处于相同温度的热浴接触的耦合量子谐振子系统的精确MFG态。 我们开发了一种非微扰方法来计算相对于MFG态的协方差。 通过与从系统吉布斯态获得的结果进行比较，我们发现与热浴耦合的影响随着距离系统-热浴边界距离的增加呈指数衰减。 这类似于最近在与环境相互作用的量子自旋链中发现的皮肤效应。 利用精确结果，我们还研究了系统与热浴之间耦合任意大的超强耦合极限，并与最近对一般量子系统得到的结果建立了联系。 显示英文摘要

摘要： An open quantum system interacting with a heat bath at given temperature is expected to reach the mean force Gibbs (MFG) state as a steady state. The MFG state is given by tracing out the bath degrees of freedom from the equilibrium Gibbs state of the total system plus bath. When the interaction between the system and the bath is not negligible, it is different from the usual system Gibbs state obtained from the system Hamiltonian only. Using the path integral method, we present the exact MFG state for a coupled system of quantum harmonic oscillators in contact with multiple thermal baths at the same temperature. We develop a nonperturbative method to calculate the covariances with respect to the MFG state. By comparing them with those obtained from the system Gibbs state, we find that the effect of coupling to the bath decays exponentially as a function of the distance from the system-bath boundary. This is similar to the skin effect found recently for a quantum spin chain interacting with an environment. Using the exact results, we also investigate the ultrastrong coupling limit where the coupling between the system and the bath gets arbitrarily large and make a connection with the recent result found for a general quantum system.