arXiv 2102.120832021-02cond-mat.stat-mechquant-ph

短时间和长时间范围内的本征态涨落定理

Eigenstate Fluctuation Theorem in the Short and Long Time Regimes

Eiki Iyoda, Kazuya Kaneko, Takahiro Sagawa

备注：: 28 pages, 17 figures
DOI：: 10.1103/PhysRevE.105.044106

摘要：

正则系综在平衡态和非平衡态的统计力学中起着至关重要的作用。例如，涨落定理的标准推导依赖于热浴的初始状态是正则系综的假设。另一方面，统计力学基础的最新进展揭示了热平衡态不一定由正则系综描述，而是可以是量子纯态，甚至是单能量本征态，如本征态热化假设（ETH）所表述的。然后，一个问题是这两个图片，正则系综和一个单一的能量本征态作为一个热平衡状态，是如何兼容的涨落定理。在本文中，我们从理论上和数值计算表明，涨落定理在长时间和短时间的制度，即使当浴的初始状态是一个单一的能量本征态的多体系统。我们在长时间范围内的波动定理的证明是基于ETH，而之前在短时间范围内基于Lieb-Robinson约束和ETH [Phys. Rev. Lett. 119，100601（2017）]。这些时间制度的证明在理论上是独立的和互补的，这意味着在整个时域的波动定理。我们还进行了系统的数值模拟的硬核玻色子的精确对角化和验证的涨落定理在这两个时间制度，通过专注于有限尺寸标度。我们的结果有助于理解涨落定理从量子多体系统的幺正动力学中出现的机制，并且可以通过实验来检验，例如，超冷原子。

英文摘要：

The canonical ensemble plays a crucial role in statistical mechanics in and out of equilibrium. For example, the standard derivation of the fluctuation theorem relies on the assumption that the initial state of the heat bath is the canonical ensemble. On the other hand, the recent progress in the foundation of statistical mechanics has revealed that a thermal equilibrium state is not necessarily described by the canonical ensemble but can be a quantum pure state or even a single energy eigenstate, as formulated by the eigenstate thermalization hypothesis (ETH). Then, a question raised is how these two pictures, the canonical ensemble and a single energy eigenstate as a thermal equilibrium state, are compatible in the fluctuation theorem. In this paper, we theoretically and numerically show that the fluctuation theorem holds in both of the long and short-time regimes, even when the initial state of the bath is a single energy eigenstate of a many-body system. Our proof of the fluctuation theorem in the long-time regime is based on the ETH, while it was previously shown in the short-time regime on the basis of the Lieb-Robinson bound and the ETH [Phys. Rev. Lett. 119, 100601 (2017)]. The proofs for these time regimes are theoretically independent and complementary, implying the fluctuation theorem in the entire time domain. We also perform a systematic numerical simulation of hard-core bosons by exact diagonalization and verify the fluctuation theorem in both of the time regimes by focusing on the finite-size scaling. Our results contribute to the understanding of the mechanism that the fluctuation theorem emerges from unitary dynamics of quantum many-body systems, and can be tested by experiments with, e.g., ultracold atoms.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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