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Scattering a pulse from a chaotic cavity: transitioning from algebraic to exponential decay
James A Hart1, Thomas M Antonsen, Edward Ott
1Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20740, USA.
Summary
Scattered power in chaotic cavities transitions from power-law to exponential decay for finite pulses. This transition is universal and depends on a normalized crossover time, revealing insights into cavity dynamics.
Area of Science:
- Physics
- Quantum Optics
- Wave Phenomena
Background:
- Lossless chaotic cavities exhibit power-law decay for ensemble-averaged scattered power at large times.
- Finite duration pulses in single cavity realizations initially follow this power-law decay.
- A transition to exponential decay is observed in individual cavity realizations for finite pulses.
Purpose of the Study:
- To investigate the transition from power-law to exponential decay for scattered power in a single realization of a chaotic cavity coupled to a single port.
- To determine the universality of this transition for different pulse shapes.
- To define and utilize a crossover time to characterize the transition.
Main Methods:
- Numerical simulations of wave scattering in lossless chaotic cavities.
- Analysis of scattered power decay for single cavity realizations with finite duration pulses.
- Definition and application of a normalized crossover time for analyzing the transition.
Main Results:
- The transition from power-law to exponential decay is explored for single-port coupled chaotic cavities.
- The transition properties are found to be universal for a given pulse shape when time is properly normalized.
- A crossover time is defined as when deviations in reflected power equal the mean reflected power.
- The probability distribution function of reflected power depends only on time normalized to this crossover time.
Conclusions:
- The transition in scattered power decay for finite pulses in chaotic cavities is a universal phenomenon.
- A normalized crossover time effectively characterizes this transition, simplifying the analysis of reflected power distributions.
- This work provides a deeper understanding of wave dynamics and scattering in complex resonant systems.
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