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Wave function structure in two-body random matrix ensembles

Kaplan1, Papenbrock

  • 1Institute for Nuclear Theory and Department of Physics, University of Washington, Seattle, Washington 98195, USA.

Physical Review Letters
|September 16, 2000
PubMed
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Eigenstate structure in random matrix ensembles shows significant deviations from theory, indicating localization in Fock space. Analytical formulas derived from scar theory accurately predict these findings in many-body fermion systems.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter physics

Background:

  • Random matrix theory (RMT) is a powerful tool for describing complex quantum systems.
  • Understanding the structure of many-body eigenstates is crucial for characterizing quantum chaos and localization phenomena.
  • Deviations from RMT predictions in interacting systems often signal underlying physical mechanisms not captured by standard models.

Purpose of the Study:

  • To investigate the structure of eigenstates in two-body interaction random matrix ensembles.
  • To identify and quantify deviations from standard random matrix theory expectations.
  • To develop an analytical framework for understanding these deviations, particularly localization effects.

Main Methods:

  • Analysis of two-body interaction random matrix ensembles.

Related Experiment Videos

  • Investigation of spectral density and eigenstate properties.
  • Application of scar theory concepts to derive analytical predictions.
  • Numerical simulations of many-body fermion systems.

    • Main Results:

    • Observed significant deviations from random matrix theory in eigenstate structure.
    • Identified prominent deviations in the tails of the spectral density, suggesting Fock space localization.
    • Derived an analytical formula connecting wave function intensity fluctuations to interaction matrix element fluctuations.
    • Demonstrated excellent agreement between theoretical predictions and numerical results for fermion systems.

    Conclusions:

    • The structure of eigenstates in interacting random matrix ensembles deviates significantly from RMT predictions.
    • Fock space localization is a key feature in the tails of the spectral density.
    • The developed analytical theory, inspired by scar theory, successfully describes these phenomena in many-body systems.