Localization of resonance eigenfunctions on quantum repellers

Abstract

We introduce a new phase space representation for open quantum systems. This is a very powerful tool to help advance in the study of the morphology of their eigenstates. We apply it to two different versions of a paradigmatic model, the baker map. This allows to show that the long-lived resonances are strongly scarred along the shortest periodic orbits that belong to the classical repeller. Moreover, the shape of the short-lived eigenstates is also analyzed. Finally, we apply an antiunitary symmetry measure to the resonances that permits to quantify their localization on the repeller.

4 pages, 4 figures

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• Structure of resonance eigenfunctions for chaotic systems with partial escape
• Short periodic orbits theory for partially open quantum maps
• Localization of Chaotic Resonance States due to a Partial Transport Barrier
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• Fractal Weyl law for Linux Kernel Architecture
• Classical transients and the support of open quantum maps
• Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
• Semiclassical Formulae For Wigner Distributions
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• The role of short periodic orbits in quantum maps with continuous openings
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• Chaos simplifies quantum friction
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• Semiclassical Limit of Resonance States in Chaotic Scattering
• Spectral behavior of contractive noise
• Classical properties of the leading eigenstates of quantum dissipative systems
• Estimating the spectral density of unstable scars
• Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization
• Scarring in open chaotic systems: The local density of states