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Thermalization has been shown to occur in a number of closed quantum many-body systems, but the description of the actual thermalization dynamics is prohibitively complex. Here, we present a model - in one and two dimensions - for which we can analytically show that the evolution into thermal equilibrium is governed by a Fokker-Planck equation derived from the underlying quantum dynamics. Our approach does not rely on a formal distinction of weakly coupled bath and system degrees of freedom. The results show that transitions within narrow energy shells lead to a dynamics which is dominated by entropy and establishes detailed balance conditions that determine both the eventual equilibrium state and the non-equilibrium relaxation to it.
The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization
Relaxation of few-body quantum systems can strongly depend on the initial state when the systems semiclassical phase space is mixed, i.e., regions of chaotic motion coexist with regular islands. In recent years, there has been much effort to understa
In statistical mechanics, a small system exchanges conserved quantities---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the conserved
Coherent many-body quantum dynamics lies at the heart of quantum simulation and quantum computation. Both require coherent evolution in the exponentially large Hilbert space of an interacting many-body system. To date, trapped ions have defined the s
We investigate the detailed properties of Observational entropy, introduced by v{S}afr{a}nek et al. [Phys. Rev. A 99, 010101 (2019)] as a generalization of Boltzmann entropy to quantum mechanics. This quantity can involve multiple coarse-grainings, e