Thesis (M.S.)--West Virginia University, 1998. / Title from document title page. "December 10, 1998." Document formatted into pages; contains viii, 64 p. Vita. Includes abstract. Includes bibliographical references (p. 60-62).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M. S.)--Chemistry and Biochemistry, Georgia Institute of Technology, 2009. / Committee Chair: Sherrill, C. David; Committee Member: Bredas, Jean-Luc; Committee Member: El-Sayed, Mostafa A.; Committee Member: Harvey, Stephen C; Committee Member: Hernandez, Rigoberto.

Thesis (M. S.)--Chemistry and Biochemistry, Georgia Institute of Technology, 2006. / Bredas, Jean-Luc, Committee Member ; Sherrill, C. David, Committee Chair ; Hernandez, Rigoberto, Committee Member.

Orientador: Bruto Max Pimentel Escobar. / Coorientador: Jeferson de Lima Tomazelli. / Doutor

No description available.

A fundamental understanding of ultrafast nonequilibrium dynamical processes in molecular aggregates is crucially important for the design of nanodevices that utilize quantum mechanical effects. However, understanding the coupled electron-phonon dynamics of such high-dimensional systems remains a challenging issue. As a result of the ever-growing computational power that is available, realistic parameterization of model Hamiltonians and implementation of sophisticated quantum dynamics algorithms have become indispensable tools for gaining insight into these processes. The focus of this dissertation is the development and implementation of approximate path integral-based methods to compute the time-evolution as well as linear and nonlinear spectroscopic signals of molecular aggregates following photo-excitation. The developments and applications presented here are geared toward gaining a better understanding of the role that electron-phonon coupling plays in framing ultrafast excitation energy transfer networks in photosynthetic light-harvesting complexes. The ultrafast excitation energy transfer dynamics that occurs upon photo-excitation of a network of electronically coupled chromophores is remarkably sensitive to the strength of electronic coupling as well as the frequencies and coupling strengths that characterize electron-phonon interactions. Based on approximations to the diabatic representation of molecular Hamiltonians, energetic models of condensed phase molecular aggregates can be parameterized from a first principles description. Often times, computational parameterization of these models reveals comparable magnitudes for intermolecular electronic couplings and electron-phonon couplings, negating the applicability of popular perturbative algorithms (such as those based on Forster or Redfield theory) for describing their time-evolution. Moreover, non-perturbative exact methods (e.g. stochastic Schrodinger equations and the Hierarchical Equations of Motion) are generally inefficient for all but a few specific limiting forms of electron-phonon coupling, or make assumptions about autocorrelation timescales of the vibrational environment. Because of the failure of the energetic parameters determined through recent ab initio studies of natural molecular aggregates to abide by the rather restrictive requirements for efficient application of the above-mentioned methods, the development of approximate non-perturbative algorithms for predicting nonequilibrium dynamical properties of such systems is a central theme in this dissertation. Following a general introductory section describing the basic concepts that are fundamental to the remainder of the thesis, the derivation of path integral dynamics methods is presented. These include a cartesian phase space path integral derivation of the truncated Wigner approximation as applied to the Meyer-Miller-Stock-Thoss mapping model for describing vibronic systems as well as a novel derivation of the Partially Linearized Density Matrix algorithm, highlighting its emergence as a leading order approximation to an, in principle, exact expression for the density matrix. An algorithm for computing the nonlinear response function for higher-order optical spectroscopy signals is presented within the framework of the partially linearized density matrix formalism. Time-resolved two-dimensional electronic spectra are computed and compared with exact results as well as standard perturbation theory-based results, highlighting the accuracy and efficiency of the developed method. Additionally, the recently popularized symmetrical quasi-classical method for computing the reduced density matrix dynamics is extended for computing linear optical spectroscopy signals, and compared with results from the partially linearized density matrix treatment. A generalization of the model Hamiltonian form utilized in recent ab initio studies is presented, allowing for direct vibrational energy relaxation due to coupling between intramolecular normal modes and their environment. The consequences of including these interactions within a model Hamiltonian that is inspired by energetic parameters found in studies of a photosynthetic light-harvesting complex are highlighted in the context of density matrix dynamics and time-resolved two-dimensional electronic spectroscopy. The results indicate that this physical process can be utilized as a means of optimizing the efficiency of excitation energy transfer and localization. Inspired by ab initio characterization of model Hamiltonians for molecular aggregates, a new approximate semiclassical propagator for describing the time-evolution of a system consisting of discrete electronic states in the presence of both high-frequency harmonic vibrational modes as well as slow environmental DOFs with arbitrary potentials is presented. Results indicate that this algorithm provides a more accurate description in this parameter regime than standard linearized path integral methods such as the partially linearized density matrix algorithm and the truncated Wigner approximation. Finally, preliminary results of dynamics involving non-perturbative field-matter interactions is presented with emphasis on strategically shaped pulses, field design through optimal control, and non-perturbative pump-probe spectroscopy.

This thesis presents an identification scheme for the dynamic model of a ship at sea. We determine the form of the governing differential equations for a ship which is free to pitch and roll, but constrained in all other degrees of freedom, using a perturbation-energy technique. This technique approximates energy expressions and applies Lagrange's equations for quazi-coordinates to develop the equations of motion. When formulating the energies, we take advantage of the ship's symmetry to reduce the number of terms. The equations of motions are approximated such that they contain quadratic and cubic nonlinear terms. Having the form of the governing equations, we set up the parametric identification procedure. Using the method of multiple scales, we exploit resonances and obtain expressions containing subsets of the parameters to be identified. Then we outline a scheme which uses these expressions in conjunction with experimental data to identify the ship parameters. / M.S.

In chip level testing using hardware description language approach, a difficult question to answer is: What is the best micro-operation perturbation for modeling fault at the chip level? In this thesis, an automatic evaluation system is developed to determine the best micro-operation perturbation. The measure used is the gate level stuck-at fault coverage achieved by the tests derived to cover the micro-operation perturbation faults. For small combinational circuits, it is shown that perturbing the elements into the logic dual is a good choice. For large combinational circuits, it is shown that there is very little variation in the gate level coverage achieved by the various microoperation faults. In this case, if coverage is to be improved, the micro-operation perturbation method must be augmented by other techniques. / Master of Science

Ultracold atoms in optical lattices offer an important tool for studying dynamics in many-body interacting systems in a pristine environment. This thesis focuses on three theoretical works motivated by recent optical lattice experiments. In the first, we theoretically study the center of mass dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center of mass motion even with insulating states in the center. We identify short and long-time mechanisms for edge state transport in insulating phases. We also argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our zero temperature results offer important insights into mechanisms of transport of atoms in trapped optical lattices while putting bounds on center of mass dynamics expected at non-zero temperature. In the second work, we study the domain wall expansion dynamics of strongly interacting bosons in 2D optical lattices with disorder in a recent experiment {[}J.-y. Choi et al., Science 352, 1547 (2016)]. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system. The last work features our study of phase diagrams of the 2D Bose-Hubbard model in an optical lattice with synthetic spin-orbit coupling. We investigate the transitions between superfluids with different phase patterns, which may be detected by measuring the spin-dependent momentum distribution. / Ph. D. / Ultracold atoms in optical lattices, a periodic potential generated by laser beams, offer an important tool for quantum simulations in a pristine environment. Motivated by recent optical lattice experiments with the implementation of disorder and synthetic spin-orbit coupling, we utilize Gutzwiller mean-field theory (GMFT) to study the dynamics of disordered state in an optical lattice under the sudden shift of the harmonic trap, the domain wall expansion of strongly interacting bosons in 2D lattices with disorder, and spin-orbit-driven transitions in the Bose-Hubbard model. We argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our findings show that evidence for many-body localization claimed in experiments [J.-y. Choi et al., Science 352, 1547 (2016)] must lie in the differences between GMFT and experiments. We also find that strong spin-orbit coupling alone can generate superfluids with finite momentum and staggered phase patterns.