Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Theological reflection at work: A phenomenological study of learning processes

Using the learning descriptions of graduates of a graduate ministry program, the mechanisms of interactions between the knowledge facets in learning processes were explored and described. The intent of the study was to explore how explicit, implicit, and emancipatory knowledge facets interacted in the learning processes at or about work. The study provided empirical research on Yang's (2003) holistic learning theory. ^ A phenomenological research design was used to explore the essence of knowledge facet interactions. I achieved epoche through the disclosure of assumptions and a written self-experience to bracket biases. A criterion based, stratified sampling strategy was used to identify participants. The sample was stratified by graduation date. The sample consisted of 11 participants and was composed primarily of married (n = 9), white, non-Hispanic (n = 10), females (n = 9), who were Roman Catholic (n = 9). Professionally, the majority of the group were teachers or professors (n = 5). ^ A semi-structured interview guide with scheduled and unscheduled probes was used. Each approximately 1-hour long interview was digitally recorded and transcribed. The transcripts were coded using a priori codes from holistic learning theory and one emergent code. The coded data were analyzed by identifying patterns, similarities, and differences under each code and then between codes. Steps to increase the trustworthiness of the study included member checks, coding checks, and thick descriptions of the data. ^ Five themes were discovered including (a) the difficulty in describing interactions between knowledge facets; (b) actual mechanisms of interactions between knowledge facets; (c) knowledge facets initiating learning and dominating learning processes; (d) the dangers of one-dimensional learning or using only one knowledge facet to learn; and (e) the role of community in learning. The interpretation confirmed, extended, and challenged holistic learning theory. Mechanisms of interaction included knowledge facets expressing, informing, changing, and guiding one another. Implications included the need for a more complex model of learning and the value of seeing spirituality in the learning process. The study raised questions for future research including exploring learning processes with people from non-Christian faith traditions or other academic disciplines and the role of spiritual identity in learning. ^

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Conjugated Quantum Dots Inhibit the Amyloid β (1–42) Fibrillation Process

Nanoparticles have enormous potential in diagnostic and therapeutic studies. We have demonstrated that the amyloid beta mixed with and conjugated to dihydrolipoic acid- (DHLA) capped CdSe/ZnS quantum dots (QDs) of size approximately 2.5 nm can be used to reduce the fibrillation process. Transmission electron microscopy (TEM) and atomic force microscopy (AFM) were used as tools for analysis of fibrillation. There is a significant change in morphology of fibrils when amyloid β (1–42) (Aβ (1–42)) is mixed or conjugated to the QDs. The length and the width of the fibrils vary under modified conditions. Thioflavin T (ThT) fluorescence supports the decrease in fibril formation in presence of DHLA-capped QDs.

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). In the present work, we follow the method originally proposed by Van Vliet in LRT. The Hamiltonian in this approach is of the form: H = H°(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H° - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H°(E, B) , include the external fields without any limitation on strength. In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0 , t → ∞ , so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices.