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Observation of Wigner-Dyson level statistics in a classically integrable system
Ahmed A Elkamshishy1, Chris H Greene2
1Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA.
Physical Review. E
|July 17, 2021
Summary
Particle transmission through disordered lattices exhibits surprising quantum chaos statistics. State localization length governs the transition from Poisson to Wigner-Dyson level statistics in these 1D systems.
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.
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