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Gradient Echo Quantum Memory in Warm Atomic Vapor
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Quantum chaotic fluctuation-dissipation theorem: Effective Brownian motion in closed quantum systems.

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  • 1Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH, United Kingdom.

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This study analytically describes how quantum systems reach equilibrium after a random matrix perturbation. It reveals a fluctuation-dissipation theorem, applicable to quantum simulations and measuring system dynamics.

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Area of Science:

  • Quantum statistical mechanics
  • Non-equilibrium dynamics
  • Condensed matter theory

Background:

  • Understanding thermalization in isolated quantum systems is a key challenge.
  • Nonintegrable systems are crucial for studying realistic quantum dynamics.
  • Random matrix theory provides models for complex quantum behavior.

Purpose of the Study:

  • To analytically describe the decay to equilibrium of observables in nonintegrable systems after a random matrix perturbation.
  • To derive an analytic form for time-averaged fluctuations related to equilibrium decay rates.
  • To establish a connection between quantum dynamics and classical fluctuation-dissipation theorems.

Main Methods:

  • Analytical description of observable decay to equilibrium.
  • Derivation of time-averaged fluctuations using decay rates.
  • Numerical experiments on a spin chain for validation.
  • Application of random matrix theory to quantum systems.

Main Results:

  • An analytic form for the decay to equilibrium of generic observables was obtained.
  • A fluctuation-dissipation theorem analogous to the Ornstein-Uhlenbeck process was derived.
  • Analytic predictions were validated through numerical simulations on a spin chain.
  • A method to measure the density of states in non-equilibrium dynamics was proposed.

Conclusions:

  • The study provides a theoretical framework for understanding quantum thermalization dynamics.
  • The derived fluctuation-dissipation relation offers a tool for experimental verification in quantum simulations.
  • The findings bridge theoretical predictions with experimental capabilities in quantum physics.
  • The work contributes to understanding non-equilibrium dynamics and density of states in isolated quantum systems.