From open quantum systems to open quantum maps

Abstract

For a class of quantized open chaotic systems satisfying a natural dynamical assumption, we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite dimensional operators obtained by quantizing the Poincaré map associated with the flow near the set of trapped trajectories.

53 pages, 8 figures

References in corpus (3)

• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Semiclassical structure of chaotic resonance eigenfunctions
• Dynamical model for the quantum-to-classical crossover of shot noise

Cited by in corpus (13)

• Spectral problems in open quantum chaos
• Resonance projectors and asymptotics for r-normally hyperbolic trapped sets
• Resonances for open quantum maps and a fractal uncertainty principle
• Observational Constraints on Modified Chaplygin Gas in Horava-Lifshitz Gravity
• Weyl law for open systems with sharply divided mixed phase space
• Resonance spectra for quantum maps of kicked scattering systems by complex scaling
• Spectral gap for obstacle scattering in dimension 2
• Fractal Weyl laws for asymptotically hyperbolic manifolds
• Mathematical Study of Scattering Resonances
• Resolvent estimates in strips for obstacle scattering in 2D and local energy decay for the wave equation
• Semi-classical quantum maps of semi-hyperbolic type
• Semi-classical quantization rules for a periodic orbit of hyperbolic type
• Quantum transfer operators and quantum scattering