A quantum cluster approach to vibrational spectra and anderson localization of phonons in disordered harmonic lattices

Abstract

The venerable phenomenon of Anderson localization (AL)[1; 2; 3; 4; 5; 6; 7] has generated a sustained interest in the condensed matter physics community over the last ve decades due to its paramount importance in diverse phenomena such as metalinsulator transitions, quantum Hall e ect, mesoscopic uctuations in small conductors, quantum chromodynamics, and quantum chaos. Although the initial focus was on electronic systems, where the quantum nature of electrons was necessary to obtain an understanding, it was quickly realized subsequently, that AL is not limited to electrons; In fact, the phenomenon should be observable with any kind of wave - quantum or classical. This thesis aims to understand the localization of phonons through a new formalism that was originally developed for electronic systems. We have organized this chapter as follows: In section 1.1, we present a general description of AL. In section 1.2, we demonstrate how the concepts of AL can explain various experimentally observed anomalous transport phenomena. In section 1.3, we discuss several direct experimental ndings of AL.