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Exact distribution of spacing ratios for random and localized states in quantum chaotic systems
Tekur S.H., , Santhanam M.S.
Published in American Physical Society
2018
PMID: 30011473
Volume: 97
   
Issue: 6
Abstract
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra are modeled through an appropriate ensemble described by random matrix theory. However, a small subset of states violates this principle and displays eigenstate localization, a counterintuitive feature known to arise due to purely quantum or semiclassical effects. In the spectrum of chaotic systems, the localized and random states interact with one another and modify the spectral statistics. In this work, a 3×3 random matrix model is used to obtain exact results for the ratio of spacing between a generic and localized state. We consider time-reversal-invariant as well as noninvariant scenarios. These results agree with the spectra computed from realistic physical systems that display localized eigenmodes. © 2018 American Physical Society.
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Figures & Tables (5)
  • Figure-0
    FIG. 1. (a) Energy levels of stadium billiards. Scarred levels ... Expand
  • Figure-1
    FIG. 4. Spacing ratio distribution, for g-l type spacings, ... Expand
  • Figure-2
    FIG. 3. (a) Information entropy S as a function of energy ... Expand
  • Figure-3
    FIG. 2. Spacing ratio distribution, for g-l type spacings, ... Expand
  • Figure-4
    FIG. 5. Spacing ratio distribution, for g-l type spacings, ... Expand
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