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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Statistical physics

Background:

  • Particle transmission through finite lattices with impurities is studied.
  • Despite being a classically integrable 1D system, spectral properties mimic chaotic systems.

Purpose of the Study:

  • To investigate resonance statistics in a 1D finite lattice with impurities.
  • To understand the influence of state localization on spectral statistics.

Main Methods:

  • Calculation of resonance positions using Wigner-Smith time delay and Siegert state methods.
  • Analysis of spectral properties including level spacing distribution and spectral rigidity.

Main Results:

  • The study reveals that spectral statistics transition from Poisson to Wigner-Dyson as state localization changes.
  • A dimensionless parameter effectively quantifies the degree of state localization.
  • Both Wigner-Smith time delay and Siegert state methods yield consistent resonance positions.

Conclusions:

  • The localization length significantly impacts the evolution of level statistics in disordered 1D lattices.
  • Quantum chaos statistics emerge in a classically non-chaotic system due to disorder and localization.