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Eigenstate thermalization hypothesis.

Joshua M Deutsch1

  • 1Department of Physics, University of California, Santa Cruz, CA 95064, United States of America.

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Summary
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Statistical mechanics in quantum systems is explained by the eigenstate thermalization hypothesis (ETH). Individual energy eigenstates act like statistical ensembles, a concept rooted in quantum chaos and random matrix theory.

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Area of Science:

  • Quantum statistical mechanics
  • Many-body quantum systems
  • Quantum chaos

Background:

  • Statistical mechanics for classical systems arises from chaotic dynamics and ergodicity.
  • Understanding thermalization in isolated quantum systems remains a key challenge.
  • The eigenstate thermalization hypothesis (ETH) provides a framework for this understanding.

Purpose of the Study:

  • To review the eigenstate thermalization hypothesis (ETH) in quantum systems.
  • To explain how individual energy eigenstates can represent statistical ensembles.
  • To explore the theoretical and experimental implications of ETH.

Main Methods:

  • Review of foundational work in random matrix theory (Wigner).
  • Analysis of concepts from quantum chaos.
  • Discussion of analytical and numerical studies of ETH.
  • Examination of experimental evidence in isolated quantum systems.

Main Results:

  • Individual energy eigenstates in quantum systems exhibit properties of statistical ensembles.
  • The eigenstate thermalization hypothesis (ETH) explains this behavior.
  • ETH has broad applicability, from black hole physics to condensed matter systems.

Conclusions:

  • The eigenstate thermalization hypothesis (ETH) offers an intuitive explanation for thermalization in quantum systems.
  • Understanding ETH is crucial for comprehending many-body quantum states.
  • Research continues into the breakdown of ETH and associated novel phenomena.