Short periodic orbits theory for partially open quantum maps

Abstract

We extend the semiclassical theory of short periodic orbits [Phys. Rev. E {\bf 80}, 035202(R) (2009)] to partially open quantum maps. They correspond to classical maps where the trajectories are partially bounced back due to a finite reflectivity $R$. These maps are representative of a class that has many experimental applications. The open scar functions are conveniently redefined, providing a suitable tool for the investigation of these kind of systems. Our theory is applied to the paradigmatic partially open tribaker map. We find that the set of periodic orbits that belong to the classical repeller of the open map ($R=0$) are able to support the set of long-lived resonances of the partially open quantum map in a perturbative regime. By including the most relevant trajectories outside of this set, the validity of the approximation is extended to a broad range of $R$ values. Finally, we identify the details of the transition from qualitatively open to qualitatively closed behaviour, providing an explanation in terms of short periodic orbits.

6 pages, 4 figures

References in corpus (8)

• Combining directional light output and ultralow loss in deformed microdisks
• Fractal Weyl laws for chaotic open systems
• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Fractal Weyl law for quantum fractal eigenstates
• Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems
• Quantum signatures of classical multifractal measures
• Classical transients and the support of open quantum maps
• Trace formula for dielectric cavities III: TE modes

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• Resonance states of the three-disk scattering system
• Semiclassical Limit of Resonance States in Chaotic Scattering
• Estimating the spectral density of unstable scars
• Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization