论文标题
相互作用的小系统与吉布斯状态的降低密度矩阵的紧密度
Closeness of the reduced density matrix of an interacting small system to the Gibbs state
论文作者
论文摘要
我研究了一个小量子系统的统计描述，该系统以通用形式和通用相互作用强度耦合到一个大量子环境，当时总系统处于微跨式集合所描述的平衡状态时。重点是在这种相互作用的情况下，中央系统的降低密度矩阵（RDM）与在未偶联的情况下获得的RDM之间的差异。在中央系统的哈密顿量的特征性中，表明对角线元素之间的差异主要受到总系统的最大特征函数的最大宽度的比率，以取消耦合的基础与微稳态能量壳的宽度的宽度；同时，非对角线元素之间的差异是由汉密尔顿相互作用的某些特性与中央系统相关水平间距的比率给出的。作为一种应用，给出了足够的条件，在该条件下，在系统环境相互作用下，RDM可能具有规范的吉布斯形式，不一定弱；该吉布斯状态通常包括相互作用的某些平均效应。对于与多体量子混沌系统局部相互作用的中央系统，这表明RDM通常具有GIBBS形式。我还研究了从能量壳中总系统的典型状态计算的RDM。
I study the statistical description of a small quantum system, which is coupled to a large quantum environment in a generic form and with a generic interaction strength, when the total system lies in an equilibrium state described by a microcanonical ensemble. The focus is on the difference between the reduced density matrix (RDM) of the central system in this interacting case and the RDM obtained in the uncoupled case. In the eigenbasis of the central system's Hamiltonian, it is shown that the difference between diagonal elements is mainly confined by the ratio of the maximum width of the eigenfunctions of the total system in the uncoupled basis to the width of the microcanonical energy shell; meanwhile, the difference between off-diagonal elements is given by the ratio of certain property of the interaction Hamiltonian to the related level spacing of the central system. As an application, a sufficient condition is given, under which the RDM may have a canonical Gibbs form under system-environment interactions that are not necessarily weak; this Gibbs state usually includes certain averaged effect of the interaction. For central systems that interact locally with many-body quantum chaotic systems, it is shown that the RDM usually has a Gibbs form. I also study the RDM which is computed from a typical state of the total system within an energy shell.
