Spread of highly localized wave-packet in the tight-binding lattice: Entropic and information-theoretical characterization

Abstract

The spread of a wave-packet (or its deformation) is a very important topic in quantum mechanics. Understanding this phenomenon is relevant in connection with the study of diverse physical systems. In this paper we apply various “spreading measures” to characterize the evolution of an initially localized wave-packet in a tight-binding lattice, with special emphasis on information-theoretical measures. We investigate the behavior of both the probability distribution associated with the wave packet and the concomitant probability current. Complexity measures based upon Rényi entropies appear to be particularly good descriptors of the details of the delocalization process.