Statistical Localization of Electromagnetic Signals in Disordered Time-Varying Cavity

TL;DR

This paper studies how electromagnetic signals in disordered, time-varying cavities become statistically localized and normally distributed, with findings on how energy input affects field distribution and intensity deviations.

Contribution

It introduces a statistical analysis of electromagnetic localization in disordered, time-varying cavities using probabilistic theorems, revealing new insights into field distribution and extreme event probabilities.

Findings

Electromagnetic fields tend to be normally distributed in disordered cavities with temporal disorder.

Increasing energy input leads to higher probability of extreme fields and deviation from normal distribution.

Temporal disorder can induce statistical localization of electromagnetic signals.

Abstract

In this letter, we investigate the statistical properties of electromagnetic signals after different times of duration within one-dimensional local-disordered time-varying cavities, where both spatial and temporal disorders are added. Our findings reveal that, in the vast majority of cases, adequate temporal disorder in local space can make the electromagnetic field statistically localized, obeying a normal distribution at a specific point in time of arbitrary location within the cavity. We employ the concept of disordered space-time crystals and leverage Lindeberg's and Lyapunov's theorems to theoretically prove the normal distribution of the field values. Furthermore, we find that with the increase of energy provided by time variation, the probability of extreme fields will significantly increase and the field intensity eventually is de-normalized, that is, deviating from the normal distribution. This study not only sheds light on the statistical properties of transient signals in local-disordered time-varying systems but also paves the way for further exploration in wave dynamics of analogous systems.