论文标题
统计复杂性和多体混沌量子系统中的平衡道路
Statistical complexity and the road to equilibrium in many-body chaotic quantum systems
论文作者
论文摘要
在这项工作中，我们回顾了孤立的多体相互作用量子系统中平衡问题的问题。我们特别关注量子混沌汉密尔顿人，而不是专注于渐近状态的特性以及它们如何遵守特征态热化假设的预测，而是集中于平衡过程本身，即\ emph {for equilibrium}。沿着对角集合的均衡，遵守了热力学第二定律的新兴形式，我们提供了这一事实的信息理论证明。在手头的证据中，我们表明，在对角线合奏时期，达到平衡的道路不过是层次结构。此外，我们引入了统计复杂性和熵复杂性平面的概念，我们通过比较了熵复杂性平面中的轨迹与随机汉密尔顿产生的熵 - 复合体中的轨迹，研究了通用多体系统中平衡道路的独特性。最后，通过将随机的哈密顿量视为扰动，我们分析了与混乱的哈密顿量和不同类型的初始状态相关的熵复杂性轨迹的稳定性。
In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how they adhere to the predictions of the Eigenstate Thermalization Hypothesis, we focus on the equilibration process itself, i.e., \emph{the road to equilibrium}. Along the road to equilibrium the diagonal ensembles obey an emergent form of the second law of thermodynamics and we provide an information theoretic proof of this fact. With this proof at hand we show that the road to equilibrium is nothing but a hierarchy in time of diagonal ensembles. Furthermore, introducing the notions of statistical complexity and the entropy-complexity plane, we investigate the uniqueness of the road to equilibrium in a generic many-body system by comparing its trajectories in the entropy-complexity plane to those generated by a random Hamiltonian. Finally by treating the random Hamiltonian as a perturbation we analyzed the stability of entropy-complexity trajectories associated with the road to equilibrium for a chaotic Hamiltonian and different types of initial states.
