Quantum chaotic resonances from short periodic orbits

Abstract

We present an approach to calculating the quantum resonances and resonance wave functions of chaotic scattering systems, based on the construction of states localized on classical periodic orbits and adapted to the dynamics. Typically only a few of such states are necessary for constructing a resonance. Using only short orbits (with periods up to the Ehrenfest time), we obtain approximations to the longest living states, avoiding computation of the background of short living states. This makes our approach considerably more efficient than previous ones. The number of long lived states produced within our formulation is in agreement with the fractal Weyl law conjectured recently in this setting. We confirm the accuracy of the approximations using the open quantum baker map as an example.

4 pages, 4 figures

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• Asymptotic boundary layer method for unstable trajectories: Semiclassics for individual scar wavefunctions
• Short periodic orbits theory for partially open quantum maps
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• Lagrangian descriptors for open maps
• Super-sharp resonances in chaotic wave scattering
• Multifractality of open quantum systems
• Classical transients and the support of open quantum maps
• Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
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• Transient features of quantum open maps
• The role of short periodic orbits in quantum maps with continuous openings
• Weyl law for open systems with sharply divided mixed phase space
• Lyapunov exponents and Hamiltonian poles in a non Hermitian dynamics
• Local random vector model for semiclassical fractal structure of chaotic resonance states
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• Resonance spectra for quantum maps of kicked scattering systems by complex scaling
• Resonance states of the three-disk scattering system
• Semiclassical Limit of Resonance States in Chaotic Scattering
• Semiclassical matrix elements for a chaotic propagator in the Scar functions basis
• Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization