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Universal response of quantum systems with chaotic dynamics.
Diego A Wisniacki1, Natalia Ares, Eduardo G Vergini
1Departamento de Física J. J. Giambiagi, FCEyN, UBA, and IFIBA, CONICET, Pabellón 1, Ciudad Universitaria, C1428EGA Buenos Aires, Argentina.
Physical Review Letters
|September 28, 2010
Summary
Quantum systems with chaotic dynamics exhibit a universal response to perturbations. The local density of states (LDOS) follows a Breit-Wigner distribution, revealing predictable behavior in quantum chaos.
Area of Science:
- Quantum mechanics
- Quantum chaos
- Statistical physics
Background:
- Predicting closed system responses to external perturbations is crucial in quantum mechanics.
- The local density of states (LDOS) describes system response by analyzing eigenfunction overlaps.
- Understanding quantum chaos dynamics is key to predicting system behavior.
Purpose of the Study:
- To demonstrate the universal response of quantum systems with classically chaotic dynamics.
- To show that the LDOS follows a Breit-Wigner distribution for general perturbations.
- To derive a semiclassical expression for the LDOS width in chaotic systems.
Main Methods:
- Analysis of the local density of states (LDOS) in closed quantum systems.
- Investigating systems with classically chaotic dynamics.
- Derivation of semiclassical expressions for spectral properties.
Main Results:
- The LDOS is shown to be a Breit-Wigner distribution for general perturbations in classically chaotic systems.
- A highly accurate semiclassical expression for the LDOS width is derived.
- The universality of quantum system response in the presence of chaos is demonstrated.
Conclusions:
- Quantum systems with classically chaotic dynamics exhibit universal behavior under perturbation.
- The Breit-Wigner distribution accurately describes the LDOS in these systems.
- The derived semiclassical formula provides a precise tool for analyzing quantum chaos.
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