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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Chaos theory

Background:

  • Random matrix theory (RMT) is used to model complex quantum systems.
  • Nonlinear perturbations can significantly alter the dynamics of these systems.
  • Understanding thermalization in isolated quantum systems is a key challenge.

Purpose of the Study:

  • To investigate the effects of nonlinear perturbations on the time evolution of quantum systems described by RMT.
  • To identify the conditions under which dynamical thermalization occurs.
  • To characterize the system's temperature and energy distribution.

Main Methods:

  • Numerical simulations of a system of linear oscillators with nonlinear perturbations.
  • Analysis of system dynamics in relation to a 'chaos border'.
  • Application of concepts from classical statistical mechanics and Kolmogorov-Arnold-Moser integrability.

Main Results:

  • Above a chaos border, weak to moderate nonlinearity induces dynamical thermalization in a finite number of degrees of freedom.
  • Energy equipartition over linear eigenmodes is observed, consistent with classical statistical mechanics.
  • System temperature exhibits a broad range, including positive and negative values, dependent on initial energy.
  • Below the chaos border, dynamics adhere to Kolmogorov-Arnold-Moser integrability.

Conclusions:

  • The study reveals generic properties of nonlinear perturbations in RMT systems due to universal features.
  • Dynamical thermalization is a key phenomenon emerging from nonlinear interactions in quantum chaotic systems.
  • The findings bridge quantum dynamics with classical statistical mechanics principles.