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Quantum chaotic fluctuation-dissipation theorem: effective Brownian motion in closed quantum systems
journal contribution
posted on 2023-06-09, 19:56 authored by Charlie Nation, Diego PorrasWe analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable in terms of the rate of decay to equilibrium. Our result shows the emergence of a Fluctuation-Dissipation theorem corresponding to a classical Brownian process, specifically, the Ornstein-Uhlenbeck process. Our predictions can be tested in quantum simulation experiments, thus helping to bridge the gap between theoretical and experimental research in quantum thermalization. We test our analytic results by exact numerical experiments in a spin-chain. We argue that our Fluctuation-Dissipation relation can be used to measure the density of states involved in the non-equilibrium dynamics of an isolated quantum system.
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Publication status
- Published
File Version
- Accepted version
Journal
Physical Review EISSN
1539-3755Publisher
American Physical SocietyExternal DOI
Issue
5Volume
99Article number
a052139Department affiliated with
- Physics and Astronomy Publications
Research groups affiliated with
- Atomic, Molecular and Optical Physics Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2020-02-03First Open Access (FOA) Date
2020-02-03First Compliant Deposit (FCD) Date
2020-02-01Usage metrics
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