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Concentration of quantum equilibration and an estimate of the recurrence time
by Jonathon Riddell, Nathan J. Pagliaroli, Álvaro M. Alhambra
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Submission summary
| Authors (as registered SciPost users): | Alvaro Alhambra · Jonathon Riddell |
| Submission information | |
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| Preprint Link: | scipost_202301_00012v2 (pdf) |
| Date accepted: | 2023-09-13 |
| Date submitted: | 2023-06-21 18:11 |
| Submitted by: | Riddell, Jonathon |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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 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.
Published as SciPost Phys. 15, 165 (2023)
Reports on this Submission
Report 2 by Lorenzo Campos Venuti on 2023-9-5 (Invited Report)
Strengths
Same as previous
Report
The authors have satisfactorily answered all my comments. I therefore encourage publication of the manuscript.
Minor point/typo, here are still a few occurrences of <A(\infty)>.