Our first paper of 2019 “Dirac wave transmission in Lévy disordered systems” has just been accepted for publication in Physical Review E, an American Physical Society journal.
In this paper we investigate the propagation of electronic waves described by the Dirac equation subject to a certain disorder distribution. The disorder takes the form of potential barriers following an unusual statistical distribution, know as the Lévy distribution. Our numerical calculations reveal a phase transition from anomalous to standard to anomalous localization as the incidence energy increases. In contrast, electronic waves described by the Schrödinger equation do not present such transition. We obtain the phase diagram delimiting anomalous and standard localization regimes, and argue that these transitions can also be characterized by the dispersion of the transmission. We attribute the transition to an abrupt reduction in transmittance when the incidence angle is higher than a critical value, which induces a decrease in transmission fluctuations.
This work is a collaboration with Jonas R. F. Lima and Anderson L. R. Barbosa, both at Universidade Federal Rural de Pernambuco. A.L.R. Barbosa was also my graduate school colleague at UFPE back in 2003-2005. Networking does pay off.