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Nonequilibrium Dynamics and Weakly Broken Integrability.

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We present a quantum kinetic approach for understanding the real-time dynamics of weakly perturbed integrable models. This method reveals specific perturbations that prevent thermalization in quantum systems.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Atomic physics

Background:

  • Dynamical experiments on cold atomic gases provide motivation.
  • Integrable models are a key focus in quantum many-body physics.
  • Understanding systems out of equilibrium is a significant challenge.

Purpose of the Study:

  • To develop a quantum kinetic approach for real-time dynamics of weakly perturbed integrable models.
  • To analyze prethermalization and late-time thermalization regimes.
  • To establish analytical predictions for physical quantities and thermalization rates.

Main Methods:

  • Utilizing exact matrix elements of the underlying integrable model.
  • Developing an analytical approach for real-time quantum dynamics.
  • Connecting perturbed quantum many-body dynamics with classical Kolmogorov-Arnold-Moser theory.

Main Results:

  • The approach covers a broad range of timescales, from prethermalization to thermalization.
  • Predictions for effective temperatures and thermalization rates are provided.
  • A family of perturbations that do not induce thermalization was identified.

Conclusions:

  • The developed quantum kinetic approach offers insights into the dynamics of quantum systems.
  • The findings link quantum many-body theory with classical chaos theory.
  • Specific perturbations can prevent thermalization in weakly perturbed integrable systems.