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Quantum systems self-consistently thermalize via a "thermalization front" that separates initial conditions from equilibrium. This process, understood through dynamical mean-field theory (DMFT), reveals how isolated systems lose memory and reach thermal equilibrium.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Physics

Background:

  • Isolated quantum many-body systems are expected to thermalize, acting as their own thermal baths.
  • This self-thermalization leads to loss of initial condition memory and local subsystem equilibrium.

Purpose of the Study:

  • To investigate the framework of dynamical mean-field theory (DMFT) for understanding self-consistent thermalization.
  • To analyze the emergence of a self-consistent bath in quantum lattice models.

Main Methods:

  • Utilized the infinite-dimensional limit of quantum lattice models within DMFT.
  • Employed the Fermi-Hubbard model as a specific case study.
  • Derived a traveling wave equation of the Fisher-Kolmogorov-Petrovsky-Piskunov type for effective temperature dynamics.

Main Results:

  • Demonstrated that self-consistent bath emergence occurs via a ballistic "thermalization front."
  • This front separates the initial state from the long-time thermal fixed point.
  • The derived traveling wave equation accurately predicts the front's asymptotic shape and velocity, matching DMFT numerics.

Conclusions:

  • DMFT provides a natural framework for understanding self-consistent thermalization in isolated quantum systems.
  • The concept of a thermalization front offers a new perspective on the onset of quantum thermalization.
  • The derived traveling wave equation serves as a predictive tool for thermalization dynamics.