Summary |
This thesis consists of two parts. Part I is related to the subject in theoretical quan-tum statistical dynamics, while Part II concerns about the statistical mechanics approach to protein folding problems. In Part I, we report our development of quantum dissipation theory (QDT) and applications. In the aspect of theoretical development, we construct various second-order formulations in the weak system-bath coupling regime, and further an exact theory applicable to arbitrary non-Markovian bath interaction. We also develop an exact, nonperturbative electron transfer theory, and elucidate some im-portant issues, such as the quantum solvation effect in relation to reaction mecha-nism, and the complex dependence of both kinetics and thermodynamics on solvent environment. In the application aspect, we consider the optical spectroscopy and laser control of molecular dynamics, besides the electron transfer problems. The details of Part I are as follows. Chapter 1 presents an overview on the early development of quantum dissipa-tion theory, together with some basic knowledge and techniques on non-dissipative quantum mechanics. In chapter 2, besides the well-established linear response theory and fluctuation-dissipation theorem, we construct also the exact theory of driven Brownian oscil-lator (DBO). Considered here is a harmonic system, coupled linearly with an arbi-trary harmonic bath and an arbitrary external field. The exact DBO results and their implications will be exploited later in the development of approximated QDT formalism in general. Propose in this chapter is also a parameterization scheme for the efficient treatment of non-Markovian interaction bath effects on the reduced system dynamics, both approximate and exact, to be developed soon. In chapter 3, we report our development on various complete second-order QDT (CS-QDT) formalisms. In particular, we propose a novel CS-QDT construction, in which the dissipation superoperator is separated into field-free and field-dressed parts, and then treat the former in a memory-free prescription while the latter in terms of memory kernel. Both the initial system-bath coupling and the correlated non-Markovian dissipation and external field drive effects are treated properly within the second-order level. Various forms of CS-QDT differ at their resum-mation schemes that partially include high order system-bath coupling effects. On the basis of the comparison with the exact DBO results, together with the consideration of numerical stability and efficiency, the aforementioned unconven-tional CS-QDT form is found to be the overall best among various approximation schemes. Applications of the CS-QDT are made to some optical response and control of molecular dynamics processes. In chapter 4, we construct an exact QDT, via direct calculus on Feynman-Vernon dissipation functionals. The resulting theory, in terms of hierarchically coupled differential equations of motion (EOM) instead of path integral, facilitates the numerical study of quantum dissipation that is in general nonperturbative and non-Markovian. We further construct the equivalent continued fraction formalism, allowing the quantum dissipation be resolved efficiently in an inward-recursive manner. Chapter 5 focuses on our revisit of the elementary electron transfer (ET) pro-cess, on the basis of the exact reduced density matrix dynamics theory developed in chapter 4. An analytical and exact expression for the ET rate in Debye solvents at finite temperature is further arrived by using the Dyson equation technique. Not only does it recover the celebrated Marcus' inversion and Kramers' turnover behaviors of the ET reaction rate, the new theory also predicts some interesting and unexplored characteristics of equilibrium thermodynamics functions as their dependence on the solvent environment. The nature solvation, quantum versus classical, is also investigated in its relation to the distinct ET mechanics. The concluding remarks on Part I, the development of QDT and its applica-tions, will be deferred to the end of the thesis. In Part II, we develop a mean-field Ising model to study protein folding prob-lems. Implementation are made to not only the thermal and chemical response, but also the mechanical response of the protein folding-unfolding experiments. In this model, proteins are represented topologically by the Ising model. The key quantities of the study are the order parameters that described the folding prob-abilities of individual two-state peptide bonds or other units that consists of the protein. Chapter 6 presents some theoretical background on proteins folding, together with the basis knowledge about the structures and functions of proteins. In chapter 7, we construct a mean-field theory for both the thermodynamics and kinetics of protein folding-unfolding in the absence of the external mechanical force. The resulting formalisms are apply to analyze experimental observations of various proteins. We also show that the simple uniform formulations can summarize a number of experimental measured equilibrium and kinetics behaviors in terms of two universal plots. In chapter 8, we further develop a statistical force-extension model. We apply this model to analyze our own force-extension experimental results on ubiquitin tetramers, and also that on titin reported in literature. Chapter 9 reports some experimental results on horse heart oxidized cytochrome c obtained from different spectroscopic methods. The free energy parameters ob-tained by fitting with our model are found to be dependent on experiment methods due to the different units being measured. Finally in chapter 10, we present the brief remarks to conclude this work, together with the possible direction to the further development of each theme covered in this thesis. |