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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Classical ergodicity and quantum eigenstate thermalization: Analysis in fully connected Ising ferromagnets.

Takashi Mori1

  • 1Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan.

Physical Review. E
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Classical ergodicity and quantum eigenstate thermalization are linked in Ising ferromagnets. For spin-1 systems, quantum eigenstate expectation values match classical dynamics averages, crucial for understanding thermalization in semiclassical systems.

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Area of Science:

  • Statistical mechanics
  • Quantum physics
  • Condensed matter theory

Background:

  • Investigating the connection between classical ergodicity and quantum eigenstate thermalization.
  • Examining fully connected Ising ferromagnets with varying spin values.

Purpose of the Study:

  • To explore the relationship between classical dynamics and quantum thermalization.
  • To understand the conditions under which quantum systems reach thermal equilibrium.

Main Methods:

  • Analysis of spin-1/2 and spin-1 Ising ferromagnets.
  • Application of the Wentzel-Kramers-Brillouin approximation for spin-1/2.
  • Comparison of expectation values in energy eigenstates with long-time classical averages.

Main Results:

  • For spin-1/2, quantum expectation values match classical averages via Wentzel-Kramers-Brillouin approximation.
  • For spin-1, classical dynamics may not be ergodic, yet quantum and classical statistics align in the thermodynamic limit.
  • This alignment holds for random initial states sampled uniformly from the classical phase space.

Conclusions:

  • The study reveals a general property in semiclassical systems linking quantum thermalization to classical dynamics.
  • The findings are vital for comprehending equilibration, thermalization, and dynamical transitions.
  • The results highlight the role of classical ergodicity in quantum system behavior.