Concentration of quantum equilibration and an estimate of the recurrence time

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

doi:10.21468/SciPostPhys.15.4.165

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Concentration of quantum equilibration and an estimate of the recurrence time

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Alhambra, Álvaro M.
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;

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2206.07541v1.pdf
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6482.pdf
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引用

Riddell, J., Pagliaroli, N., & Alhambra, Á. M. (2023). Concentration of quantum equilibration and an estimate of the recurrence time. SciPost Physics, 15:. doi:10.21468/SciPostPhys.15.4.165.

引用: https://hdl.handle.net/21.11116/0000-000A-B709-E

要旨

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.