Wigner distribution, Wigner entropy, and Anomalous Transport of a Generalized Aubry-André model

Abstract: In this paper, we study a generalized Aubry-Andr\'{e} model with tunable quasidisordered potentials. The model has an invariable mobility edge that separates the extended states from the localized states. At the mobility edge, the wave function presents critical characteristics, which can be verified by finite-size scaling analysis. Our numerical investigations demonstrate that the extended, critical, and localized states can be effectively distinguished via their phase space representation, specially the Wigner distribution. Based on the Wigner distribution function, we can further obtain the corresponding Wigner entropy and employ the feature that the critical state has the maximum Wigner entropy to locate the invariable mobility edge. Finally, we reveal that there are anomalous transport phenomena between the transition from ballistic transport to the absence of diffusion.