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Necessity of Eigenstate Thermalization.

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This summary is machine-generated.

The eigenstate thermalization hypothesis (ETH) is sufficient for quantum systems to reach thermal equilibrium. This study proves ETH is also necessary for thermalization, establishing it as the definitive criterion for thermal behavior in quantum systems.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • The eigenstate thermalization hypothesis (ETH) posits that quantum systems equilibrate to thermal ensembles after a quantum quench.
  • ETH is widely accepted as a sufficient condition for thermalization.

Purpose of the Study:

  • To investigate whether the eigenstate thermalization hypothesis (ETH) is also a necessary condition for thermalization.
  • To establish a definitive criterion for determining thermal behavior in quantum systems.

Main Methods:

  • Analysis of quantum systems coupled to baths with defined macroscopic temperatures.
  • Mathematical derivation to prove the necessity of ETH for thermalization.

Main Results:

  • Demonstrated that if all product states of a quantum system thermalize, then the ETH must hold.
  • Established that ETH is not only sufficient but also a necessary condition for thermalization.

Conclusions:

  • The study definitively settles the question of thermal behavior in quantum systems.
  • Determining if a quantum system exhibits thermal behavior can be reduced to checking if its Hamiltonian satisfies the ETH.