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Concentration of quantum equilibration and an estimate of the recurrence time

Jonathon Riddell, Nathan J. Pagliaroli, Álvaro M. Alhambra

SciPost Phys. 15, 165 (2023) · published 16 October 2023


We show that the dynamics of generic quantum systems concentrate around their equilibrium value when measuring at arbitrary times. This means that the probability of finding such values away from that equilibrium is exponentially suppressed, with a decay rate given by the effective dimension. Our result allows us to place a lower bound on the recurrence time of quantum systems, since recurrences corresponds to the rare events of finding a state away from equilibrium. In many-body systems, this bound is doubly exponential in system size. We also show corresponding results for free fermions, which display a weaker concentration and earlier recurrences.

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