Scattering a pulse from a chaotic cavity: Transitioning from algebraic to exponential decay

TL;DR

This paper investigates how the power scattered from a chaotic cavity transitions from a power-law decay to an exponential decay over time, revealing universal behavior when normalized appropriately.

Contribution

It characterizes the universal transition behavior of scattered power in chaotic cavities for finite pulses and defines the crossover time based on deviations from the mean.

Findings

Transition from power-law to exponential decay identified

Universal properties of the transition depend only on normalized time

Probability distribution of reflected power depends solely on normalized time

Abstract

The ensemble averaged power scattered in and out of lossless chaotic cavities decays as a power law in time for large times. In the case of a pulse with a finite duration, the power scattered from a single realization of a cavity closely tracks the power law ensemble decay initially, but eventually transitions to an exponential decay. In this paper, we explore the nature of this transition in the case of coupling to a single port. We find that for a given pulse shape, the properties of the transition are universal if time is properly normalized. We define the crossover time to be the time at which the deviations from the mean of the reflected power in individual realizations become comparable to the mean reflected power. We demonstrate numerically that, for randomly chosen cavity realizations and given pulse shapes, the probability distribution function of reflected power depends only on time, normalized to this crossover time.