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.

Originally 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 (1)

• Open circular billiards and the Riemann hypothesis

Cited by in corpus (6)

• Poincare recurrences and transient chaos in systems with leaks
• Poincare recurrences from the perspective of transient chaos
• Escape from attracting sets in randomly perturbed systems
• Faster than expected escape for a class of fully chaotic maps
• Effect of noise in open chaotic billiards
• Escape Dynamics of Many Hard Disks