Abstract
The time that waves spend inside 1D random media with the possibility of performing Lévy 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—Lévy 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 Lévy walks. Our results reveal a universal character of wave propagation that goes beyond standard Brownian wave-diffusion.
Highlights
A wave packet launched into a scattering region can penetrate that region and it may be reflected eventually
The delay time has received attention in many disciplines since it reveals information on the scattering medium and, it has been of interest from an application point of view; e.g., the delay time is a fundamental quantity in imaging of tissues in optical coherence tomography[3,4]
Since disorder is ubiquitous in real systems, there has been a great interest in studying the effects of Anderson localization on dynamical quantities such as the delay time
Summary
A wave packet launched into a scattering region can penetrate that region and it may be reflected eventually. The inverse square power decay of the distribution of τR has been predicted in semi-infinite 1D s ystems[11] and studied in higher d imensions[12,13,14]. Another example is the average delay time, which is proportional to the mean length of trajectories[15]. This quantity was predicted to be invariant with respect to details of the scattering region, as recently observed experimentally[15,16,17]
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