Quantum thermalization and multi-temperature models

Quantum thermalization, i.e., how an isolated quantum system can dynamically reach thermal equilibrium behavior, is a long-standing problem of quantum statistics. The eigenstate thermalization hypothesis (ETH) poses that, under certain conditions, the long-time expectation value w.r.t. a typical energy eigenstate is indistinguishable from a microcanonical average. This precludes describing the dynamical approach to equilibrium. By contrast, in a sufficiently complex, nonintegrable system (characterized by a vast Hilbert space dimension D), any experiment defines a partitioning into the measured quantum numbers and the remaining Hilbert subspace. The entanglement entropy of this measured system reaches a maximum by tracing out the unobserved subspace, which acts as a grand-canonical bath [Ann. Phys. 1700124 (2018)]. We find, that the approach to the thermodynamic limit is controled by the size of D rather than the particle number. We show thermalization and grand-canonical behavior of fluctuations for a bose gas and for small Fermi-Hubbard clusters. For the latter, we consider spin and charge as the subsystems in the above sense and investigate the temperature dynamics. They are well described by rate equations for spin and charge temperatures with an exponential memory kernel.