Eigenstate thermalization in interacting quantum gases in optical lattices

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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.