Quantum chaotic fluctuation-dissipation theorem: effective Brownian motion in closed quantum systems

Nation, Charlie and Porras, Diego (2019) Quantum chaotic fluctuation-dissipation theorem: effective Brownian motion in closed quantum systems. Physical Review E, 99 (5). a052139. ISSN 1539-3755

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Abstract

We 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Research Centres and Groups: Atomic, Molecular and Optical Physics Research Group
Subjects: Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics > QC0174.12 Quantum theory. Quantum mechanics
Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics > QC0174.8 Statistical physics
Depositing User: Charlie Nation
Date Deposited: 03 Feb 2020 12:18
Last Modified: 03 Feb 2020 12:30
URI: http://sro.sussex.ac.uk/id/eprint/88764

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