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Loschmidt echo and the local density of states
Natalia Ares1, Diego A Wisniacki
1Departamento de Física J J Giambiagi, FCEN, UBA, Ciudad Universitaria, Buenos Aires, Argentina.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
Loschmidt echo (LE) decay reveals quantum system reversibility. Unexpected non-uniform decay rates, influenced by local density of states (LDOS) oscillations and local perturbations, challenge predictions based solely on Lyapunov exponents in chaotic systems.
Area of Science:
- Quantum chaos
- Statistical mechanics
- Dynamical systems
Background:
- Loschmidt echo (LE) quantifies reversibility and sensitivity to perturbations in quantum dynamics.
- Weak perturbations correlate LE decay with the local density of states (LDOS) width.
- Strong perturbations in chaotic systems were expected to yield decay governed by the Lyapunov exponent.
Purpose of the Study:
- Investigate the non-uniform LE decay regime observed in recent studies.
- Analyze the behavior of perturbed cat maps under varying perturbation strengths.
- Clarify the influence of local perturbations on LE decay dynamics.
Main Methods:
- Studied perturbed cat maps as a model system.
- Analyzed the decay rate of the Loschmidt echo.
- Examined the relationship between LE decay, LDOS, and perturbation strength.
Main Results:
- Observed that some perturbations induce coherent oscillations in LDOS width.
- These LDOS oscillations imprint clear signals on the LE decay.
- Local perturbations, acting on small phase space regions, significantly magnify effects, leading to LE decay governed by LDOS width.
Conclusions:
- The study reveals a complex interplay between perturbation strength, LDOS, and LE decay in chaotic systems.
- Coherent LDOS oscillations and localized perturbations offer explanations for non-uniform LE decay.
- Findings challenge the universal applicability of Lyapunov exponents for strong perturbations in all chaotic quantum systems.
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