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. ^

Deprofessionalization of curriculum decision -making

The purpose of this study was to analyze the evolution of Florida state level policy efforts and to assess the responding educational policy development and implementation at the local school district level. The focus of this study was the secondary language arts curriculum in Miami-Dade County Public Schools. ^ Data was collected using document analysis as a source of meaning making out of the language sets proffered by agencies at each level. A matrix was created based on Klein's levels of curriculum decision-making and Functional Process Theory categories of policy formation. The matrix allowed the researcher to code and classify specific information in terms accountability/high-stakes testing; authority; outside influences; and operational/structural organization. ^ Federal policy documents provided a background and impetus for much of what originated at the State level. The State then produced policy directives which were accepted by the District and specific policy directives and guidelines for practice. No evidence was found indicating the involvement of any other agencies in the development, transmission or implementation of the State level initiated policies. ^ After analyzing the evolutionary process, it became clear that state policy directives were never challenged or discussed. Rather, they were accepted as standards to be met and as such, school districts complied. Policy implementation is shown to be a top-down phenomenon. No evidence was found indicating a dialogue between state and local systems, rather the state, as the source of authority, issued specifically worded policy directives and the district complied. Finally, this study recognizes that outside influences play an important role in shaping the education reform policy in the state of Florida. The federal government, through NCLB and other initiatives created a climate which led almost naturally to the creation of the Florida A+ Plan. Similarly, the concern of the business community, always interested in the production of competent workers, continued to support efforts at raising the minimum skill level of Florida high school graduates. ^ Suggestions are made for future research including the examination of local school sites in order to assess the overall nature of the school experience rather than rely upon performance indicators mandated by state policy. ^

Deprofessionalization of curriculum decision-making

The purpose of this study was to analyze the evolution of Florida state level policy efforts and to assess the responding educational policy development and implementation at the local school district level. The focus of this study was the secondary language arts curriculum in Miami-Dade County Public Schools. Data was collected using document analysis as a source of meaning making out of the language sets proffered by agencies at each level. A matrix was created based on Klein's levels of curriculum decision-making and Functional Process Theory categories of policy formation. The matrix allowed the researcher to code and classify specific information in terms accountability/high-stakes testing; authority; outside influences; and operational/structural organization. Federal policy documents provided a background and impetus for much of what originated at the State level. The State then produced policy directives which were accepted by the District and specific policy directives and guidelines for practice. No evidence was found indicating the involvement of any other agencies in the development, transmission or implementation of the State level initiated policies. After analyzing the evolutionary process, it became clear that state policy directives were never challenged or discussed. Rather, they were accepted as standards to be met and as such, school districts complied. Policy implementation is shown to be a top-down phenomenon. No evidence was found indicating a dialogue between state and local systems, rather the state, as the source of authority, issued specifically worded policy directives and the district complied. Finally, this study recognizes that outside influences play an important role in shaping the education reform policy in the state of Florida. The federal government, through NCLB and other initiatives created a climate which led almost naturally to the creation of the Florida A+ Plan. Similarly, the concern of the business community, always interested in the production of competent workers, continued to support efforts at raising the minimum skill level of Florida high school graduates. Suggestions are made for future research including the examination of local school sites in order to assess the overall nature of the school experience rather than rely upon performance indicators mandated by state policy.

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.

Network Construction and Graph Theoretical Analysis of Functional Language Networks in Pediatric Epilepsy

This dissertation introduces a new approach for assessing the effects of pediatric epilepsy on the language connectome. Two novel data-driven network construction approaches are presented. These methods rely on connecting different brain regions using either extent or intensity of language related activations as identified by independent component analysis of fMRI data. An auditory description decision task (ADDT) paradigm was used to activate the language network for 29 patients and 30 controls recruited from three major pediatric hospitals. Empirical evaluations illustrated that pediatric epilepsy can cause, or is associated with, a network efficiency reduction. Patients showed a propensity to inefficiently employ the whole brain network to perform the ADDT language task; on the contrary, controls seemed to efficiently use smaller segregated network components to achieve the same task. To explain the causes of the decreased efficiency, graph theoretical analysis was carried out. The analysis revealed no substantial global network feature differences between the patient and control groups. It also showed that for both subject groups the language network exhibited small-world characteristics; however, the patient’s extent of activation network showed a tendency towards more random networks. It was also shown that the intensity of activation network displayed ipsilateral hub reorganization on the local level. The left hemispheric hubs displayed greater centrality values for patients, whereas the right hemispheric hubs displayed greater centrality values for controls. This hub hemispheric disparity was not correlated with a right atypical language laterality found in six patients. Finally it was shown that a multi-level unsupervised clustering scheme based on self-organizing maps, a type of artificial neural network, and k-means was able to fairly and blindly separate the subjects into their respective patient or control groups. The clustering was initiated using the local nodal centrality measurements only. Compared to the extent of activation network, the intensity of activation network clustering demonstrated better precision. This outcome supports the assertion that the local centrality differences presented by the intensity of activation network can be associated with focal epilepsy.