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. ^

The effects on students' self-efficacy beliefs regarding their comprehension of American literature when aesthetic reading and reader response strategy are implemented

High-stakes testing and accountability have infiltrated the education system in the United States; the top priority for all teachers must be student progress on standardized tests. This has resulted in the predominance of reading for test-taking, (efferent reading), in the English, language arts, and reading classrooms. Authentic uses of print activities, like aesthetic reading, that encourage students to engage individually with a text, have been pushed aside. ^ During a 3-week time period, regular level, English 3/American literature students in a Title I magnet high school, participated in this quasi-experimental study (N = 62). It measured the effects of an intervention of reading American literature texts aesthetically and writing aesthetically-evoked reader responses on students' self-efficacy beliefs regarding their comprehension of American literature. One trained teacher and the researcher participated in the study: student participants were pre- and post- tested using the Confidence in Reading American Literature Survey which examined their self-efficacy beliefs regarding their comprehension of American literature. Several statistical analyses were performed. The results of the linear regression analyses partially supported a positive relationship between aesthetically-evoked reader responses and students' self-efficacy beliefs regarding their comprehension of American literature. Additionally, the results of the 2 (sex) x 2 (treatment) ANCOVAs conducted to test group differences in self-efficacy beliefs regarding the comprehension of American literature between treatment and control groups indicated a main effect for treatment (but not sex; nor was there a significant sex x treatment interaction), suggesting the treatment was partially effective in increasing students' self-efficacy beliefs. Seven of the twelve ANCOVAs indicated a statistically significant increase in the treatment group's adjusted group mean self-efficacy belief scores as a result of being exposed to the intervention. In six of these seven analyses, increases in self-efficacy beliefs occurred in tasks that required three or more higher-order levels of thinking/learning. The results are discussed in terms of theoretical, empirical and practical significance. Future research is recommended to extend the intervention beyond the narrow confines of a Title I magnet school to settings where the intervention could be tested longitudinally, e. g., honors and gifted students, elementary and middle schools.^

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.

The Effects on Students' Self-Efficacy Beliefs Regarding Their Comprehension of American Literature When Aesthetic Reading and Reader Response Strategy are Implemented

High-stakes testing and accountability have infiltrated the education system in the United States; the top priority for all teachers must be student progress on standardized tests. This has resulted in the predominance of reading for test-taking, (efferent reading), in the English, language arts, and reading classrooms. Authentic uses of print activities, like aesthetic reading, that encourage students to engage individually with a text, have been pushed aside. During a 3-week time period, regular level, English 3/American literature students in a Title I magnet high school, participated in this quasi-experimental study (N = 62). It measured the effects of an intervention of reading American literature texts aesthetically and writing aesthetically-evoked reader responses on students’ self-efficacy beliefs regarding their comprehension of American literature. One trained teacher and the researcher participated in the study: student participants were pre- and post- tested using the Confidence in Reading American Literature Survey which examined their self-efficacy beliefs regarding their comprehension of American literature. Several statistical analyses were performed. The results of the linear regression analyses partially supported a positive relationship between aesthetically-evoked reader responses and students’ self-efficacy beliefs regarding their comprehension of American literature. Additionally, the results of the 2 (sex) x 2 (treatment) ANCOVAs conducted to test group differences in self-efficacy beliefs regarding the comprehension of American literature between treatment and control groups indicated a main effect for treatment (but not sex; nor was there a significant sex x treatment interaction), suggesting the treatment was partially effective in increasing students’ self-efficacy beliefs. Seven of the twelve ANCOVAs indicated a statistically significant increase in the treatment group’s adjusted group mean self-efficacy belief scores as a result of being exposed to the intervention. In six of these seven analyses, increases in self-efficacy beliefs occurred in tasks that required three or more higher-order levels of thinking/learning. The results are discussed in terms of theoretical, empirical and practical significance. Future research is recommended to extend the intervention beyond the narrow confines of a Title I magnet school to settings where the intervention could be tested longitudinally, e. g., honors and gifted students, elementary and middle schools.