Our latest publication of 2022 “Wave transmission and its universal fluctuations in one-dimensional systems with Lévy-like disorder: Schrödinger, Klein-Gordon, and Dirac equations”  has just appeared in the Physical Review E.

In this publication we investigate the propagation of electronic waves in one-dimensional systems with Lévy-type disorder. We perform a complete analysis of nonrelativistic and relativistic wave transmission submitted to potential barriers whose width, separation, or both follow Lévy distributions characterized by an exponent 0<α<1. For the first two cases, where one of the parameters is fixed, nonrelativistic and relativistic waves present anomalous localization. However, for the latter case, in which both parameters follow a Lévy distribution, nonrelativistic and relativistic waves present a transition between anomalous and standard localization as the incidence energy increases relative to the barrier height. Moreover, we obtain the localization diagram delimiting anomalous and standard localization regimes, in terms of incidence angle and energy. Finally, we verify that transmission fluctuations, characterized by its standard deviation, are universal, independent of barrier architecture, wave equation type, incidence energy, and angle, further extending earlier studies on electronic localization. We believe that our predictions can be verified in graphene nanoribbons, where Dirac electrons are the main charge carriers.

This publication was done in collaboration with Jonas R.F. Lima and Anderson L. R. Barbosa, both at UFRPE, and we began it before the covid-19 pandemic hit the world! We are all glad to finally see it out there.

New article in Physical Review E: Wave transmission in Lévy-disordered systems