Universal statistics of waves in a random time-varying medium

TL;DR

This paper demonstrates that waves in a randomly fluctuating time-varying medium exhibit universal statistical behaviors, with energy distributions transitioning from exponential to log-normal over time, supported by theory and simulations.

Contribution

It introduces a universal statistical framework for wave energy distribution in time-varying disordered media, bridging space and time disorder studies.

Findings

Energy distribution is log-normal at long times.

Energy follows a negative exponential distribution at short times.

Theoretical predictions match numerical simulations.

Abstract

We study the propagation of waves in a medium in which the wave velocity fluctuates randomly in time. We prove that at long times, the statistical distribution of the wave energy is log-normal, with the average energy growing exponentially. For weak disorder, another regime preexists at shorter times, in which the energy follows a negative exponential distribution, with an average value growing linearly with time. The theory is in perfect agreement with numerical simulations, and applies to different kinds of waves. The existence of such universal statistics bridges the fields of wave propagation in time-disordered and space-disordered media.