非周期性足以实现宏观热化
Aperiodicity is sufficient for macroscopic thermalization
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中文总结 AI 辅助
该研究提出非周期性机制，可基于初始态量子动力学的非周期性，在有限时间内预测宏观可观测量的热化，将宏观热化纳入可操作量子统计力学范畴，能提供有限时间的可靠预测。
中文摘要 AI 辅助
我们针对宏观可观测量（如粗粒化电荷密度）的有限时间热化识别出一种通用机制，该机制基于初始态量子动力学的基本形式：（1）非周期性，它为（2）希尔伯特空间的动力学部分遍历探索提供了可计算的度量。具体而言，该机制仅在初始态系综的返回概率在有限时间范围内较小这一与可观测量无关的信息下，就可预测有限及更长区间内几乎所有初始系综的态、几乎所有时间下所有（集中的）宏观可观测量的平衡。作为特例，它还能通过初始态在能量本征基中离域化的有效维度（更强版本）得到无限长时间平衡的标准结果。我们的研究将宏观热化纳入了近期发展的可操作量子统计力学范畴，该领域旨在为微观热化提供有限可计算判据。我们讨论了该方法的整体特征：建立了（1）指示无记忆性的（理论或实验上）可计算探针的衰减、（2）希尔伯特空间中可观测量或态对齐的基本不变机制、（3）预测不同自然形式的（经典及）量子热化三者间的联系，其中多数严格将基于本征态的无限时间热化的常规描述作为特例恢复，且在热力学极限下能对有限观测时间提供更可靠的可及预测。
英文摘要
We identify a general mechanism for the finite-time thermalization of macroscopic observables, such as coarse-grained charge densities, in terms of elementary forms of the quantum dynamics of initial states: (1) aperiodicity, which provides a computable measure of (2) a dynamical partially ergodic exploration of the Hilbert space. Specifically, this mechanism predicts the equilibration of all (concentrated) macroscopic observables, in almost all states in an initial ensemble and almost all times within finite and longer intervals, given only the observable-independent information that the return probability of the ensemble of initial states is small over a finite time range. As a special case, it also accesses standard results on equilibration over infinitely long times in terms of (stronger versions of) the effective dimension of initial state delocalization in the energy eigenbasis. Our results incorporate macroscopic thermalization into the domain of operational quantum statistical mechanics, recently developed to provide finitely computable criteria for microscopic thermalization. We discuss an overall characterization of this approach as establishing connections between (1) the decay of a (theoretically or experimentally) computable probe indicating memorylessness, (2) a fundamental invariant mechanism in terms of the alignment of observables or states in the Hilbert space, and (3) predicting different natural forms of (classical and) quantum thermalization, most of which rigorously recover conventional eigenstate-based descriptions of infinite-time thermalization as a special case but provide stronger accessible predictions over finite observation times in the thermodynamic limit.
发表机构
- JILA and Center for Theory of Quantum Matter, Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系量子物质理论中心及JILA）
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