Eigenstate thermalization in interacting quantum gases in optical lattices

封闭量子系统中热化和驰豫的理论描述需要考虑其完整的量子力学动力学，需要对量子混沌的定义和对量子浴的表征。本征态热化假说为基于多体哈密顿本征态和局域可观测量性质的一般热化行为的预测提供了充分的判据。在本研究单位的实验中，验证本征态热化假说的预测是我们的主要目标之一。理论项目T2将与实验团队密切合作，解决三个目标。首先，我们将分析实验相关模型中局域观测的非对角本征态矩阵元，目的是在定量水平上预测弛豫动力学和相关的时间尺度。其次，我们将通过考虑在两分量Bose-Hubbard系统中实现的微扰可积自旋系统来研究高温下扩散输运的出现和潜在的流体动力学描述。最后，我们将研究光学晶格中的质量不平衡费米气体，目的是识别作为密度和质量不平衡的函数的慢动力学的遍历区域和可能的参数区域。这个项目将使用精确对角化和密度矩阵重整化群方法。

The theoretical description of thermalization and relaxation in closed quantum systems needs to account for their full quantum-mechanical dynamics, requires a definition of quantum chaos and a characterization of quantum baths. The eigenstate thermalization hypothesis provides sufficient criteria to predict generic thermalizing behavior based on the knowledge of many-body Hamiltonian eigenstates and properties of local observables. Verifying predictions from the eigenstate thermalization hypothesis in the experiments of this Research Unit is one of our key goals. The theory project T2 will address three objectives, in close collaboration with experimental teams. First, we will analyze the off-diagonal eigenstate matrix elements of local observables in experimentally relevant models, aiming at predicting the relaxation dynamics and the relevant time scales on a quantitative level. Second, we will study the emergence of diffusive transport and an underlying hydrodynamical description at high temperatures by considering perturbed integrable spin systems, realized in two-component Bose-Hubbard systems. Finally, we will study mass-imbalanced Fermi gases in optical lattices, aiming at identifying ergodic regimes and possibly also parameter regimes of slow dynamics as a function of density and mass imbalance. This project will employ exact diagonalization and density matrix renormalization group methods.