Eigenstate thermalization hypothesis, time operator, and extremely quick relaxation of fidelity
Eigenstate thermalization hypothesis, time operator, and extremely quick relaxation of fidelity
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DOI：
10.1088/2399-6528/aad223
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发表时间：
2018-02
影响因子：
1.2
通讯作者：
T. Monnai
中科院分区：
文献类型：
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作者：
T. Monnai
本征态热化假说 (ETH) 指出，对于不可积系统，每个能量本征态准确地给出一类可观测量的微正则期望值。在本文中，我们从时间-能量不确定性和操作定义的“时间算子”的大多数准本征态所共有的内在热性质方面探讨了 ETH：首先，我们证明能量本征态是无数个适当定义的“时间算子”的准本征态的叠加。大多数此类准本征态对于热力学隔离量子多体系统来说是热的，并且在保真度的极短弛豫时间方面近似正交。通过这种方式，我们的场景提供了 ETH 的理论解释。
The eigenstate thermalization hypothesis (ETH) states that for nonintegrable systems, each energy eigenstate accurately gives microcanonical expectation values for a class of observables. In this paper, we explore the ETH in terms of the time-energy uncertainty and an intrinsic thermal nature shared by the majority of quasi eigenstates of operationally defined ‘time operator’: First, we show that the energy eigenstates are superposition of uncountably many quasi eigenstates of suitably defined ‘time operator’. Majority of such quasi eigenstates are thermal for thermodynamic isolated quantum many-body systems and approximately orthogonal in terms of extremely short relaxation time of the fidelity. In this manner, our scenario provides a theoretical explanation of ETH.