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Classical transients and the support of open quantum maps
Gabriel G Carlo1, D A Wisniacki, Leonardo Ermann
1Departamento de Física, Comisión Nacional de Energía Atómica, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina. carlo@tandar.cnea.gov.ar
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 16, 2013
Summary
In open quantum systems, the classical repeller may not always support semiclassical quantization. Numerical evidence shows limitations in describing resonance eigenfunctions, suggesting new elements are needed for semiclassical theory.
Area of Science:
- Quantum mechanics
- Classical dynamics
- Statistical physics
Background:
- Semiclassical theory relies on classical invariant objects for quantization.
- Classical repellers are widely believed to support quantization in open scattering systems.
- Previous studies focused on quantum maps to understand this relationship.
Purpose of the Study:
- To investigate the role of classical repellers in semiclassical theory for open scattering systems.
- To examine if classical repellers universally support quantization in these systems.
- To identify limitations of current semiclassical descriptions.
Main Methods:
- Numerical analysis of recently introduced tribaker maps.
- Comparison of maps with identical asymptotic properties but different short-time behaviors.
- Analysis of eigenvalue distributions and resonance eigenfunctions of the evolution operator.
Main Results:
- Eigenvalue distributions of the studied maps adhere to the fractal Weyl law.
- The theory of short periodic orbits for open maps fails to describe resonance eigenfunctions in some cases.
- This discrepancy highlights limitations in the current semiclassical description.
Conclusions:
- The classical repeller may not always be the appropriate object for semiclassical quantization in open systems.
- New theoretical elements are required to enhance the semiclassical description of open quantum systems.
- Further research is needed to incorporate these new elements and refine the theory.
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