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Most isolated quantum systems reach thermal equilibrium if their observable A meets the weak eigenstate thermalization hypothesis (wETH). This dynamical typicality approach confirms thermalization for systems not in small initial states.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • Understanding thermalization in isolated quantum systems is a fundamental challenge.
  • The eigenstate thermalization hypothesis (ETH) provides a theoretical framework for thermalization.
  • The weak eigenstate thermalization hypothesis (wETH) offers a relaxed condition for thermalization.

Purpose of the Study:

  • To investigate the conditions under which isolated many-body quantum systems thermalize.
  • To establish a link between the observable's properties and the system's thermalization behavior.
  • To explore the validity of the weak eigenstate thermalization hypothesis (wETH) in generic quantum systems.

Main Methods:

  • Employing a dynamical typicality approach.
  • Analyzing initial states within a microcanonical energy shell.
  • Considering systems with fixed nonequilibrium expectation values for an observable A.

Main Results:

  • Demonstrating that most initial states exhibit thermalization if and only if the observable A satisfies wETH.
  • Showing that thermalization occurs when the observable's expectation value remains close to the microcanonical value over time.
  • Confirming that wETH implies similar expectation values for A across most energy eigenstates.

Conclusions:

  • The weak eigenstate thermalization hypothesis (wETH) is a crucial condition for thermalization in isolated quantum systems.
  • Dynamical typicality provides a powerful tool for understanding thermalization in quantum statistical mechanics.
  • The study clarifies the relationship between microscopic properties (eigenstates) and macroscopic behavior (thermalization).