Relaxation and Spectra in Condensed Phases

In this thesis, various problems in the quantum theory of relaxation are considered. We first discuss the dynamics of low temperature tunneling in condensed phases. With the aid of a varational unitary transformation, we are able to study the limits of both weak and strong coupling of the tunneling system to the environment. Next we discuss the physical implications of the standard Redfield equations when perturbation theory is carried out to fourth order. We then apply similar techniques to the study of the spin-boson problem. Here, various methods of aproximate resummation are used to calculate the mean position of a tunneling particle coupled to a fluctuating quantum environment. The next section deals with a theoretical attempt to explain recent hole burning experiments in a low temperature polymer glass. The last section deals with the nonperturbative theory of pure dephasing. Thesis Supervisor: Robert J. Silbey Title: Professor of Chemistry Acknowledgments First and foremost, I would like to thank my thesis advisor, Bob Silbey. Bob's keen insights, knowledge, and good humor were always helpful. I thank him most for the reminder "99 percent of the time that you think you'll fail, you'll be alright, the one time out of one hundred that you do fall flat on your face, only you will remember." I would like to thank professor Irwin Oppenheim. Irwin was always willing to answer my questions and listen to ideas, no matter how naive. I would also like to thank Irwin, as well as professor Bruce Tidor, for helping out with applications and recommendations. I would like to thank Professor Min Cho, Dr. Peter Neu and Dr. Alberto Suarez for helpful discussions and scientific collaborations. Some of these collaborative efforts appear in this thesis. I would also like to thank my "zoo" friends, Frank Brown, Cliff Liu, Welles Morgado, Joan Shea, and Sophia Yaliraki. I would separately like to thank Frank for time spent on scientific collaboration, and computer help. I would like to thank Cliff, Sophia, and Joan for help with this thesis. I would like to thank the DOD for financial support in the years 1993-1996. Lastly, I would like to thank my parents, brother and sister for their support and love.