Probing Dynamical Anderson Transition in a Periodically‐Driven Lattice by Statistical Measures

Abstract

The Floquet system, as a platform to explore new physics in the time domain, has attracted wide interest. This paper considers the dynamical Anderson transition of a single particle in a 1D incommensurate potential, acted by periodic driving. The competition of three elements including the quasi‐disorder, periodic driving, and hopping, produces very rich yet unexplored phenomena in the system. The variance of the Shannon entropy is suggested, inspired by the fact that the Shannon entropy is just the mean information. For the ratio of nearest quasi‐eigenenergy spacings, its probability density distribution is obtained numerically. Based on this distribution, two statistical measures, the entropy of the ratio and the variance of the entropy are suggested to detect the dynamical transition. Moreover, the Anderson transition can also be identified by the pseudo‐spin operators based on the site bases.