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Generalized Thermalization in Quantum-Chaotic Quadratic Hamiltonians.

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Quantum systems achieve thermalization through equilibration and matching ensemble predictions. Even when observables equilibrate, they may not exhibit eigenstate thermalization in many-body sectors, necessitating the generalized Gibbs ensemble.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Thermalization in quantum systems requires equilibration and agreement with statistical ensembles like Gibbs or generalized Gibbs.
  • Understanding thermalization in nonintegrable and integrable systems is crucial for quantum physics.

Purpose of the Study:

  • To investigate the behavior of observables in quantum-chaotic quadratic models, specifically focusing on thermalization in many-body sectors.
  • To determine whether observables exhibiting eigenstate thermalization in single-particle sectors also do so in many-body sectors.

Main Methods:

  • Analysis of quantum-chaotic quadratic models.
  • Mathematical proof regarding the equilibration of observables.
  • Investigation of eigenstate thermalization in single-particle versus many-body sectors.

Main Results:

  • Observables exhibiting eigenstate thermalization in the single-particle sector do equilibrate in many-body sectors of quantum-chaotic quadratic models.
  • These same observables do not exhibit eigenstate thermalization in many-body sectors, with exponentially many outliers.
  • The generalized Gibbs ensemble is generally required to describe expectation values after equilibration.

Conclusions:

  • Eigenstate thermalization is not guaranteed in many-body sectors even for systems that equilibrate.
  • The generalized Gibbs ensemble, with Lagrange multipliers dependent on single-particle energies, is essential for describing thermalization in these complex quantum systems.