Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates

Abstract

One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of chaotic systems is proportional to the hole size and independent of position. Here we give exact formulas for the subsequent terms, as sums of correlation functions; these depend on hole size and position, hence yield information on the closed system dynamics. Conversely, the theory can be readily applied to experimental design, for example to control escape rates.

arXiv commentOriginally 4 pages and 2 eps figures incorporated into the text; v2 has more numerical results and discussion: now 6 pages, 4 figures

References in corpus (5)

• Observation of resonance trapping in an open microwave cavity
• Average exit times in volume preserving maps
• Open circular billiards and the Riemann hypothesis
• Mixmaster chaos
• The existence of Burnett coefficients in the periodic Lorentz gas

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• Escape Behavior of Quantum Two-Particle Systems with Coulomb Interactions
• Recurrence of particles in static and time varying oval billiards
• Intrinsic stickiness in open integrable billiards: tiny border effects
• Dependence of chaotic diffusion on the size and position of holes
• Escape from attracting sets in randomly perturbed systems
• Faster than expected escape for a class of fully chaotic maps
• Eigenfunctions of the Perron-Frobenius operator and the finite-time Lyapunov exponents in uniformly hyperbolic area-preserving maps
• Effect of noise in open chaotic billiards
• Follow the fugitive: an application of the method of images to open dynamical systems
• Quantifying intermittency in the open drivebelt billiard
• Local Escape Rates for $\varphi$-mixing Dynamical Systems
• Asymptotic expansions for the escape rate of stochastically perturbed unimodal maps
• Rotating Leaks in the Stadium Billiard
• Particle escapes in an open quantum network via multiple leads
• Quantum particle escape from a time-dependent confining potential
• Escape-rate response to noise of all amplitudes in leaky chaos
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• Escape Dynamics of Many Hard Disks
• Survival probability of random walks leaping over traps