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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Eigenstate Thermalization Hypothesis and Its Deviations from Random-Matrix Theory beyond the Thermalization Time.

Jiaozi Wang1, Mats H Lamann1, Jonas Richter2

  • 1Department of Physics, University of Osnabrück, D-49076 Osnabrück, Germany.

Physical Review Letters
|May 20, 2022
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Summary
This summary is machine-generated.

The eigenstate thermalization hypothesis suggests quantum systems equilibrate due to random matrix theory (RMT) properties. This study finds matrix elements remain correlated at thermalization timescales, challenging the RMT assumption.

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Area of Science:

  • Quantum Many-Body Physics
  • Statistical Mechanics
  • Quantum Chaos

Background:

  • The eigenstate thermalization hypothesis (ETH) explains thermal equilibrium in isolated quantum systems.
  • ETH assumes observable matrix elements in the energy eigenbasis follow random matrix theory (RMT) principles.
  • The precise energy scale at which matrix elements become uncorrelated is not fully understood.

Purpose of the Study:

  • To investigate the extent to which RMT applies to quantum many-body systems.
  • To determine the energy scale at which operator matrix elements become uncorrelated.
  • To probe correlations beyond the limits of exact diagonalization.

Main Methods:

  • Developed a novel numerical approach to analyze operator matrix element correlations.
  • Evaluated higher moments of operator submatrices within varying energy windows.
  • Studied nonintegrable quantum spin chains.

Main Results:

  • Observed persistent correlations between matrix elements even in narrow energy windows.
  • These correlations persist at energy scales relevant to observable thermalization times.
  • Demonstrated that residual correlations impact out-of-time-ordered correlation functions.

Conclusions:

  • Matrix elements in quantum many-body systems exhibit correlations beyond the predictions of standard RMT.
  • These correlations are present at timescales relevant to thermalization.
  • The findings necessitate a refinement of the ETH and RMT applicability in quantum dynamics.