Eigenstate fluctuation theorem in the short- and long-time regimes.
Eigenstate fluctuation theorem in the short- and long-time regimes.
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DOI：
10.1103/physreve.105.044106
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
E. Iyoda;K. Kaneko;T. Sagawa
中科院分区：
文献类型：
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作者：
E. Iyoda;K. Kaneko;T. Sagawa
正则系综在平衡态和非平衡态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表明，热平衡态不一定是由正则系综描述的，而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）所表述的那样。那么问题来了，这两幅图，经典系综和作为热平衡态的单一能量本征态，是如何在涨落定理中兼容的。在本文中，我们从理论上和数值上证明了涨落定理在长时间和短时间状态下都成立，即使当槽的初始状态是多体系统的单能量本征态时也是如此。我们在长时间状态下对涨落定理的证明是基于ETH的，而之前在短时间状态下对涨落定理的证明是基于Lieb-Robinson界和ETH[物理学]。[j].科学通报，2016,(5):557 - 557 . [j].科学通报。这些时间域的证明在理论上是相互独立和互补的，隐含了整个时域的涨落定理。我们还通过精确对角化对硬核玻色子进行了系统的数值模拟，并通过关注有限尺度来验证两种时间域的涨落定理。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产生的机制，并且可以通过超冷原子等实验进行验证。
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)0031-900710.1103/PhysRevLett.119.100601]. 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.