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Spectral correlations in systems undergoing a transition from periodicity to disorder
T Dittrich1, B Mehlig, H Schanz
1Departamento de Física, Universidad de los Andes, A.A. 4976, Santafé de Bogotá, Colombia.
Summary
We investigated spectral statistics in quasi-one-dimensional systems transitioning from order to disorder. Our findings show spectral properties smoothly interpolate between periodic and disordered limits, matching numerical simulations.
Area of Science:
- Condensed matter physics
- Quantum chaos
- Statistical mechanics
Background:
- Understanding spectral statistics is crucial for characterizing quantum systems.
- Quasi-one-dimensional systems offer a unique platform to study transitions from ordered to disordered behavior.
- Previous work established universal statistics for purely periodic or disordered systems.
Purpose of the Study:
- To investigate spectral statistics in systems exhibiting a transition from periodicity to disorder.
- To compute the spectral two-point form factor and its dependence on the degree of disorder.
- To bridge the gap between established theoretical frameworks for ordered and disordered systems.
Main Methods:
- Theoretical computation of the spectral two-point form factor.
- Analysis of systems interpolating between periodic and disordered regimes.
- Numerical simulations on chains of chaotic billiards and graphs.
Main Results:
- The spectral two-point form factor smoothly interpolates between Poissonian statistics (disordered case) and universal expressions (periodic case).
- The derived expression explicitly depends on the degree of disorder in the system.
- Theoretical predictions show excellent agreement with numerical results.
Conclusions:
- The study provides a unified description of spectral statistics across the order-disorder transition.
- The findings are validated by numerical data from complex systems like chaotic billiards.
- This work advances the understanding of spectral properties in finite, quasi-one-dimensional systems.
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