Concentration of quantum equilibration and an estimate of the recurrence time

Abstract

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 them away from 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.

6+6 pages, 2 figures. Comments welcome

References in corpus (4)

• Foundation of Statistical Mechanics under experimentally realistic conditions
• Gaussian Equilibration
• Benchmarking Quantum Simulators using Ergodic Quantum Dynamics
• Emergent statistical mechanics from properties of disordered random matrix product states

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• Extremal jumps of circuit complexity of unitary evolutions generated by random Hamiltonians