Theoretical studies on some classical and quantum transport problems in random media

Abstract

The problem of transport of charge (electrons, holes and ions) and energy (excitons) in a dynamically disordered medium is assuming increasing significance in recent times, from theoretical and experimental viewpoints. However, relative to the case of static disorder, namely, the Anderson localization problem, the case of the dynamic disorder has been treated much less adequately. In this thesis, we have addressed ourselves to some stochastic aspects of the problem of transport in a dynamically disordered medium. The thesis comprises four chapters, in addition to the general introduction. Chapters II through IV are concerned with the quantum and the classical transport in certain random media. Chapter V is concerned with the classical motion of a charged particle in a uniform magnetic field in the presence of the stochastic forces of a thermal bath. Since the details of the treatments and the physical contexts vary from chapter to chapter, we thought it apt to make each chapter self-contained as far as possible. Thus each chapter contains its own introduction. The purpose of the general introduction, i.e., Chapter I, is only to give an overview of the thesis and to highlight the original contributions.