Physics & Astronomy ETDs

Publication Date

Spring 5-10-2018


This dissertation is a study of the theoretical framework of the practical as well as fundamental problem of the process of relaxation to equilibrium of quantum mechanical systems. The fundamental aspect is concerned with the simultaneous occurrence of decoherence and population equilibration. The practical aspect deals with experimental observations of vibrational relaxation of molecules embedded in liquids or solids. The systems include, but are not limited to, the nondegenerate dimer and harmonic oscillator, in one case weak and in the other strong, interaction with a thermal bath. The time dependence of the energy and the temperature dependence of the relaxation rate are the specific observables addressed in this dissertation. The analysis is based on the method of generalized master equations (GMEs). The memory functions in the GME are derived from specified Hamiltonians with given, microscopically formulated, interactions with specific reservoirs. The theory is developed with the help of projections and coarse-graining operator techniques with the assumption of initial random phases. These memories are documented in the general sense in terms of the time-correlation function of the interaction potential which is the thermal average over bath states. For simple types of interaction potential, the memories can be further written in terms of components contributed separately by the system and bath. The bath contribution is an equilibrium thermal correlation function. The memories and bath correlation functions are used to calculate the time dependence of the energy of the system and the temperature dependence of the bath spectral function or relaxation rate of the system, respectively. Predictions include an interesting, perhaps unexpected, nonmonotonicity effect and oscillations of a relaxation memory with respect to temperature. The theory is briefly discussed in the context of observations of the relaxation of specified molecular-bath interactions done via pump-probe experiments. An interpolation formula for the time dependence of the energy of the relaxing molecule is developed on the basis of the half-Markoffian approximation and a result relating relaxation rates to hypergeometric functions is presented. The thesis also contains a research contribution, unrelated to its primary topic, concerning the macroscopic classical problem of the flow of granular materials.

Degree Name


Level of Degree


Department Name

Physics & Astronomy

First Committee Member (Chair)

V. M. Kenkre

Second Committee Member

Arash Mafi

Third Committee Member

James Thomas

Fourth Committee Member

Anil Prinja




vibrational relaxation theory from microscopics, approach to thermal equilibrium, nonmonotonic temperature dependence, multiphonon interaction, single-phonon interaction, polaronic transformation

Document Type