Delay time of waves performing L\'evy walks in 1D random media

Abstract

The time that waves spend inside 1D random media with the possibility of performing L\'evy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered systems via the delay time. We show that a wide class of disorder--L\'evy disorder--leads to strong random fluctuations of the delay time; nevertheless, some statistical properties such as the tail of the distribution and the average of the delay time are insensitive to L\'evy walks. Our results reveal a universal character of wave propagation that goes beyond standard Brownian wave-diffusion.