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.
