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Eigenstate thermalization and ensemble equivalence in few-body fermionic systems.

Ph Jacquod1

  • 1Department of Quantum Matter Physics, University of Geneva, CH-1211 Geneva, Switzerland and School of Engineering, University of Applied Sciences of Western Switzerland HES-SO, CH-1951 Sion, Switzerland.

Physical Review. E
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Summary
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We show that a few-fermion system

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Eigenstate thermalization hypothesis (ETH) describes how isolated quantum systems reach thermal equilibrium.
  • Understanding thermalization in small quantum systems is crucial for quantum technologies.

Purpose of the Study:

  • Investigate eigenstate thermalization in few-body fermionic systems.
  • Explore the connection between a system's eigenstates and thermodynamic properties.
  • Determine conditions for true thermal equilibrium between a few-fermion system and a probe.

Main Methods:

  • Utilizing a few-body fermionic Hamiltonian in its eigenstates.
  • Employing a weakly coupled Fermi-Dirac gas as a thermometric probe.
  • Analyzing particle and heat currents to establish equilibrium conditions.

Main Results:

  • A probe's temperature accurately reflects the few-fermion eigenstate's properties.
  • Thermodynamic relations and the zeroth law of thermodynamics are satisfied.
  • Sufficiently strong interactions lead to orbital occupancies matching the Fermi-Dirac distribution, establishing true equilibrium.

Conclusions:

  • Eigenstate thermalization in few-body systems is linked to ensemble equivalence.
  • Individual many-body eigenstates can define a microcanonical ensemble equivalent to a canonical ensemble.
  • Stronger interactions are key for achieving true thermal equilibrium and ensemble equivalence.