Dynamics and spectra in condensed phases : single molecule spectroscopy, electron transfer, and excitation energy transfer

Abstract

In this thesis, several problems regarding dynamics and spectra in condensed phases are theoretically analyzed via analytical models. The thesis consists of four main topics. First, a theoretical description of single molecule spectroscopy is presented in order to study time-dependent fluctuations of single molecule spectra in a dynamic environment. In particular, the photon counting statistics is investigated for a single molecule undergoing a generic type of spectral diffusion process. An exact analytical solution is found for this case, and various physical limits are analyzed. Second, motivated by recent experimental observations of anomalous spectral fluctuations in quantum dot systems, both the lineshape phenomenon and the photon counting statistics are explored when spectral fluctuations are characterized by power-law statistics, for which there is no finite timescale. Unique features of the power-law statistics are demonstrated in spectral properties of those systems. Third, a spectral analysis method is developed for the non-adiabatic electron transfer reactions, which allows a unified treatment of diverse kinetic regimes in the electron transfer process. The method is applied to electron transfer reactions in mixed-valence systems in order to explore the possibility of electronic coherence. Finally, effects of the nonequilibrium bath relaxation on the excitation energy transfer process are investigated by generalizing the Forster-Dexter theory of excitation energy transfer to the case of the nonstationary bath relaxation.