Physics & Astronomy ETDs

Publication Date

Fall 12-5-2016

Abstract

This dissertation is a report on a number of distinct topics in the field of non-equilibrium statistical mechanics including the evolution of classical as well as quantum systems.

The evolution of an object that is described by the Ornstein-Uhlenbeck process generalized through a time-nonlocal attraction is considered. The time-nonlocality is taken to be represented in the Langevin description through the presence of memory. Analysis of the Langevin equation is performed for algebraic and delay-type memories. An equivalent \emph{bona-fide} Fokker-Planck equation is constructed.

A random walker subjected to a non-standard confining potential, taken to be a piece-wise linear function, is analyzed. Matching conditions for arbitrary joining configurations are given. Exact propagators in both the time- and Laplace-domains are derived for the case of a `V'-shaped potential. Two illustrative applications of such calculations are presented in the areas of chemical physics and biophysics.

The relaxation of quantum systems interacting with a thermal reservoir is studied. Calculations for specified bath spectral functions are presented. Our primary focus is the vibrational relaxation of an excited molecule and we provide a generalization of the Montroll-Shuler equation into the coherent domain. A related system, the Stark ladder, is briefly discussed.

Degree Name

Physics

Level of Degree

Doctoral

Department Name

Physics & Astronomy

First Committee Member (Chair)

Vasudev Kenkre

Second Committee Member

Sudhakar Prasad

Third Committee Member

Dinesh Loomba

Fourth Committee Member

Luca Giuggioli

Language

English

Document Type

Thesis

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