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Temperature of a single chaotic eigenstate.

Fausto Borgonovi1,2, Francesco Mattiotti1, Felix M Izrailev3,4

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This study explores how isolated quantum systems of bosons reach thermal equilibrium within a single energy state. It introduces a method to define eigenstate temperature, crucial for understanding thermalization in quantum systems.

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Area of Science:

  • Quantum statistical mechanics
  • Condensed matter physics

Background:

  • Understanding thermalization in isolated quantum systems is a fundamental challenge.
  • Bose-Einstein statistics describe weakly interacting bosons.

Purpose of the Study:

  • To investigate the onset of thermalization in a closed system of interacting bosons at the single eigenstate level.
  • To establish a criterion for thermalization based on eigenstate energy.
  • To define and calculate the temperature of a single eigenstate.

Main Methods:

  • Analysis of a closed system of randomly interacting bosons.
  • Focus on the emergence of Bose-Einstein distribution for single-particle occupation numbers.
  • Development of a local criterion for thermalization dependent on eigenstate energy.

Main Results:

  • A local criterion for thermalization within a single eigenstate was established.
  • A method to define the temperature of an eigenstate was developed for chaotic eigenstates.
  • An analytical expression for eigenstate temperature was derived, dependent on interparticle interaction and energy.

Conclusions:

  • Thermalization in isolated bosonic systems can be understood at the single-eigenstate level.
  • Eigenstate temperature is a well-defined quantity for chaotic eigenstates.
  • The derived temperature depends on system interactions and energy.