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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter theory

Background:

  • Chaotic eigenstates in interacting quantum systems appear random but contain hidden correlations.
  • Berry's approach for single-particle systems provides a basis for understanding these correlations.

Purpose of the Study:

  • To lift Berry's approach into many-body space for analyzing chaotic eigenstates.
  • To identify universal signatures of many-body quantum chaos.

Main Methods:

  • Many-body semiclassical analysis applied to the mesoscopic regime.
  • Analysis of eigenstate cross-correlations and expansion coefficient distributions.
  • Comparison with extensive quantum simulations.

Main Results:

  • Identified universality in cross-correlations of chaotic many-body eigenstates.
  • Observed Gaussian distribution of expansion coefficients for these eigenstates.
  • Demonstrated that these features imprint characteristic morphology on eigenstates.

Conclusions:

  • Universality of eigenstate correlations at fixed energy density is a signature of many-body quantum chaos.
  • Findings are consistent with the eigenstate thermalization hypothesis.
  • The identified signatures extend beyond the predictions of random matrix theory.