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Correlation decay in quantum chaotic billiards with bulk or surface disorder.
E Louis1, J A Vergés, E Cuevas
1Departamento de Física Aplicada, Universidad de Alicante, Apartado 99, E-03080 Alicante, Spain.
Summary
Correlation functions in disordered quantum billiards decay exponentially. The Lyapunov exponent, characterizing this decay, is linked to disorder strength and inversely proportional to system size.
Area of Science:
- Quantum chaos
- Condensed matter physics
- Disordered systems
Background:
- Quantum billiards exhibit complex dynamics.
- Disorder significantly impacts quantum system properties.
- Correlation functions reveal system behavior over time.
Purpose of the Study:
- Investigate the decay characteristics of correlation functions in quantum billiards.
- Analyze the influence of surface and bulk disorder on these properties.
- Determine the relationship between disorder, Lyapunov exponent, and system size.
Main Methods:
- Modeling quantum systems using a tight-binding Hamiltonian with diagonal disorder.
- Solving the model on LxL square lattice clusters.
- Calculating correlation functions via time evolution of wave functions.
Main Results:
- Observed exponential decay of correlation functions.
- Established a characteristic correlation time related to the Lyapunov exponent (lambda).
- Found lambda approximately equals the imaginary part of the self-energy for low disorder.
- Demonstrated lambda is proportional to 1/L when mean free path (l) to system size (L) ratio is constant.
Conclusions:
- Disorder-induced decay in quantum billiards is governed by the Lyapunov exponent.
- The Lyapunov exponent's dependence on disorder and system size is quantified.
- Provides insights into quantum transport and localization phenomena in disordered systems.