Chaotic Systems with Absorption

Abstract

Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate $\kappa$ in terms of the natural conditionally-invariant measure of the system; (ii) an increased multifractality when compared to the spectrum of dimensions $D_q$ obtained without taking absorption and return times into account; and (iii) a generalization of the Kantz-Grassberger formula that expresses $D_1$ in terms of $\kappa$, the positive Lyapunov exponent, the average return time, and a new quantity, the reflection rate. Simulations in the cardioid billiard confirm these results.

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Cited by in corpus (11)

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• Quantum signatures of classical multifractal measures
• Localization of Chaotic Resonance States due to a Partial Transport Barrier
• Chaotic Explosions
• Local random vector model for semiclassical fractal structure of chaotic resonance states
• Probabilistic description of dissipative chaotic scattering
• Transport properties of diffusive particles conditioned to survive in trapping environments
• Consequences of a wave-correction extended ray dynamics for integrable and chaotic optical microcavities
• Counting statistics of chaotic resonances at optical frequencies: theory and experiments
• Correspondence principle, dissipation, and Ginibre ensemble
• Escape dynamics through a continuously growing leak