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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Quantum chaos

Background:

  • The eigenstate thermalization hypothesis (ETH) explains thermalization in isolated quantum systems.
  • The strong ETH posits that all energy eigenstates within a microcanonical shell exhibit thermal properties.

Purpose of the Study:

  • To numerically investigate the strong version of the ETH.
  • To evaluate the ratio of athermal energy eigenstates using large deviation properties.

Main Methods:

  • Numerical investigation of the ETH.
  • Focus on large deviation properties to quantify athermal eigenstates.
  • Analysis of finite-size scaling for nonintegrable systems.

Main Results:

  • Systematically confirmed the validity of the strong ETH, even in near-integrable systems.
  • Discovered a double exponential finite-size scaling for the ratio of athermal eigenstates in nonintegrable systems.

Conclusions:

  • The study validates the strong ETH across a range of quantum systems.
  • Large deviation analysis is a powerful tool for studying thermalization, especially with significant finite-size effects.
  • Results illuminate universal behaviors in quantum chaos.