Universal features of dynamics of localized electronic states

In a number of systems, electronic transport can be viewed as dynamics of localized electronic states. However, there is no universal theory that describes time evolution of localized states. In this work, we present universal features of such motion. They originate from the concept of adiabatic change of character near an avoided crossing. It is shown that localized electronic states move by interchanging positions with adjacent localized states that form an avoided crossing. Avoided crossings formed by two adjacent electronic states would be adiabatic, whereas avoided crossing formed by two distant electronic states would be diabatic. To illustrate this idea, we develop a numerical model based on Anderson localized states. Based on our observations, we discuss universal features of relaxation time. The presented perspective could give new insights on Metal-Insulator transitions and electron transport in nanostructures, superlattices, and disordered semiconductors.