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Random Möbius maps: Distribution of reflection in non-Hermitian one-dimensional disordered systems
Theodoros G Tsironis1, Aris L Moustakas1
1Department of Physics, National Kapodistrian University of Athens, Athens 15784, Greece.
Abstract:
Using the properties of random Möbius 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.
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