Random M\"{o}bius Maps: Distribution of Reflection in Non-Hermitian 1D Disordered Systems
Statistical Mechanics
2020-08-25 v1 Disordered Systems and Neural Networks
Mathematical Physics
math.MP
Abstract
Using the properties of random M\"{o}bius transformations, we investigate the statistical properties of the reflection coefficient in a random chain of lossy scatterers. We explicitly determine the support of the distribution and the condition for coherent perfect absorption to be possible. We show that at its boundaries the distribution has Lifshits-like tails, which we evaluate. We also obtain the extent of penetration of incoming waves into the medium via the Lyapunov exponent. Our results agree well when compared to numerical simulations in a specific random system.
Keywords
Cite
@article{arxiv.2008.10484,
title = {Random M\"{o}bius Maps: Distribution of Reflection in Non-Hermitian 1D Disordered Systems},
author = {Theodoros G. Tsironis and Aris L. Moustakas},
journal= {arXiv preprint arXiv:2008.10484},
year = {2020}
}