Generalized Thermalization in Quantum-Chaotic Quadratic Hamiltonians
Generalized Thermalization in Quantum-Chaotic Quadratic Hamiltonians
复制标题
量子混沌二次哈密顿量的广义热化
DOI：
10.1103/physrevlett.131.060401
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发表时间：
2023
影响因子：
8.6
通讯作者：
Vidmar, Lev
中科院分区：
文献类型：
--
作者：
Łydżba, Patrycja;Mierzejewski, Marcin;Rigol, Marcos;Vidmar, Lev
不可积（可积）量子系统中的热化（广义热化）需要两个要素：平衡和与吉布斯（广义吉布斯）系综预测的一致性。我们证明了量子混沌二次模型中在单粒子扇区中表现出本征态热化的观测量在多体扇区中平衡。值得注意的是，相同的观测量在多体扇区中不表现出本征态热化（我们确定有指数级的异常值）。因此，一般需要广义吉布斯系综来描述它们平衡后的期望值，并且它的特征在于拉格朗日乘子是单粒子能量的光滑函数。
Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that exhibit eigenstate thermalization in single-particle sector equilibrate in many-body sectors of quantum-chaotic quadratic models. Remarkably, the same observables do not exhibit eigenstate thermalization in many-body sectors (we establish that there are exponentially many outliers). Hence, the generalized Gibbs ensemble is generally needed to describe their expectation values after equilibration, and it is characterized by Lagrange multipliers that are smooth functions of single-particle energies.