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. ^

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.

Health beliefs and health care options of disparate black communities in the United States

According to the 1999 U.S. Census, there were approximately thirty-three million African Americans and approximately 1.8 million non-Hispanic black immigrants in the United States. The 1997 U.S. Census estimated that there were as many as 554,000 foreign-born Haitians and 505,000 foreign-born Jamaicans living in the United States, mainly residing in Florida and New York. The U.S. Census claims that blacks are one of the largest emerging ethnic groups in America constituting at least twelve percent of this country's population. Because of this increase, their specific health beliefs and health care options are increasingly nationally significant. ^ In the present intra-black and inter-ethnic study, two hundred seventy African Americans, Haitian immigrants, and Jamaican immigrants residing in South Florida were quantitatively and qualitatively surveyed in order to investigate their health beliefs and health care options. According to the reviewed literature, the three black ethnic groups researched in this study have not been compared or contrasted before in relation to these beliefs and health care choices. ^ As was discovered by the present research, differing health beliefs and health care options were the cultural products of the ethnic differences of the researched communities. It was expected that differing health beliefs among the researched black groups might indicate disparate patterns of health care utilization of either western or non-western models. Additionally, it was projected that by investigating the health beliefs and the health care options of these emerging black ethnic groups, western health care providers in the United States could become better versed in medically servicing growing ethnically-disparate black populations. The study yielded results about the researched groups that supported major findings in the reviewed literature. The data were reported and examined, and theoretical generalizations from the data were discussed. The most important of these findings was that, within a race, health beliefs and health care options were determined by specific ethno-cultural variables dependent on national origins. ^

Clash of identities in South Florida: An examination of the complexity of racial and national identity and their impact on ethnic solidarity between black Americans and Jamaicans

Immigrants from the West Indies and other nations challenge the simple United States dichotomy of blacks versus whites. Many apparently black Caribbean immigrants proclaim that they did not know they were “black” until they arrived in the U.S. They seek to maintain their national identity and resist identity and solidarity with Black Americans. In response, many Black Americans respond that the immigrants are simply being naive, that U.S. society demands simple racial identity. Regardless of one's self-identity and personal history, in the U.S., if you look black, you are black, was their thinking. ^ This study examines the contemporary struggle of identity and solidarity among and between Black Americans and Jamaicans living in South Florida (Broward and Miami-Dade counties). Even though the primary focus of this study is to examine the relationship between Black Americans and Jamaicans, other West Indian nationals will be addressed more generally. The primary research problem of this study is to determine why the existence of common ancestry and physical traits are insufficient for an assumption of ethnic solidarity between Black Americans and Jamaicans. ^ In examining this problem, I felt that depth rather than breadth would provide insight into the current state of polarization between Black Americans and Jamaicans. To this end, a qualitative study was designed. A non-random snowball sample consisting of forty-seven informants was selected for this study. Realizing that such a technique presents problems with generalizations beyond the sample, this approach was, nonetheless, the most suitable for the current research problem. One of the initial challenges of this research was the use of the label “black” in discussing Caribbean immigrants. Unlike America, where distinctions based on skin color were at the bedrock of America's formation, this was not the case in the Caribbean. In the Caribbean skin color was an important marker as an indicator of class, rather than of race. Therefore, I refrained from using the label, “black Jamaicans,” but rather used Jamaicans throughout. ^

The relationship between educational placement, instructional practices, and achievement gains of Black students with specific learning disabilities in secondary urban school settings

Black students, in general, are underserved academically (Darling-Hammond, 2000; Townsend, 2002) and overrepresented in special education (Donovan & Cross, 2002). Black students with disabilities are further overrepresented in more restrictive educational environments (Skiba, Poloni-Staudinger, Gallini, Simmons & Feggins-Azziz, 2006). Although the National Longitudinal Transition Study 2 (NLTS2) revealed that the academic performance of students with learning disabilities is positively related to the percentage of courses taken in the general education setting (Newman, 2006), the research specifically on placement of Black students with disabilities, particularly at the secondary level, as it relates to academic achievement is lacking. While previous studies have sought to determine which placement is better for students with disabilities, no study was found that specifically examined the impact of placement specific to Black students with specific learning disabilities (SLD) in urban settings (Fore, III, Hagan-Burke, Burke, Boon & Smith, 2008; Rea, McLaughlin & Walther-Thomas, 2002). This study examined educational placement, instructional best practices, and achievement gains of Black students with SLD in urban secondary settings using an ex post facto research design. Achievement, placement, and demographic data were collected and analyzed on approximately 314 Black eighth grade students with SLD. The Teacher Instructional Practices Survey was developed and used to collect and analyze data from the teachers of 78 of these students as it relates to instructional best practices. Results indicate no significant difference in reading but a significant difference in math gains of students served in inclusive settings as compared to resource settings with a small effect size. Also, no significant relationship was found between achievement gains and the reported use of instructional best practices. However, there was a relationship between educational placement and the use of instructional best practices. The results implied that there is a need for training with both general and special education teachers on instructional best practices for SWD and that there should be certain IEP team considerations when making placement decisions for this population of students with disabilities. It is recommended that future research in this area include classroom observations and factors other than test scores to measure growth in achievement.

Personal and institutional factors: Relationship to self-efficacy of persistence to the senior year in college among self-identified Black undergraduate students in a Hispanic serving institution

While undergraduate enrollment of all racial groups in United States higher education institutions has increased, 6-year graduation rates of Blacks (39%) remain low compared to other races; Asians (69%), Whites (62%), and Hispanics (50%; NCES, 2010). Women's graduation rate is higher than men's; 58% compared to men's at 53% in public institutions (IPEDS, 2011). Retention literature does not address the perceptions of Black ethnic groups' experiences in college, particularly in Hispanic serving institutions. Informed by Tinto's (1975, 1987, 1993) student academic and social integration model, Guiffrida's (2003, 2004, 2005, 2006) model of relationships while at college, and ex-post facto research design, the study investigated personal and institutional factors that relate to Black students' self-efficacy and persistence to the senior year in college. Data about Black ethnic undergraduate seniors' (N = 236) academic and social experiences in college were collected using the Student Institutional Integration Survey (SIIS), an online questionnaire. Descriptive statistics were used to collect background information about the sample, correlation was calculated to indicate the degree of relationship between the variables, and multiple linear regressions were used to identify variables that are predictors of self-efficacy of persistence. Independent samples t-test and analyses of variance were computed to determine whether differences in perceptions of personal and institutional factors that relate to self-efficacy of persistence to the senior year in college could be identified between gender and ethnicity. Frequency was summarized to identify themes of participants' primary motivation for finishing undergraduate degree programs. These themes were: (a) self-pride/personal goal, (b) professional aspiration/career (c) motivation to support family, (d) desire to have financial independence/better job, (e) to serve community, (f) opportunity to go to college, (g) being first-generation college student, and (h) prove to family the value of higher education. The research findings support the tenets of academic and social integration theories which suggest that students' interaction with peer and faculty, relationships with family and friends, and involvement in institutional activities and organizations influence their persistence in college. Implications based on the findings affect institutional policy, curriculum, and program improvements that relate to Black undergraduate students' academic and social support.

Personal and Institutional Factors: Relationship to Self-Efficacy of Persistence to the Senior Year in College among Self-Identified Black Undergraduate Students in a Hispanic Serving Institution

While undergraduate enrollment of all racial groups in United States higher education institutions has increased, 6-year graduation rates of Blacks (39%) remain low compared to other races; Asians (69%), Whites (62%), and Hispanics (50%; NCES, 2010). Women’s graduation rate is higher than men’s; 58% compared to men’s at 53% in public institutions (IPEDS, 2011). Retention literature does not address the perceptions of Black ethnic groups’ experiences in college, particularly in Hispanic serving institutions. Informed by Tinto’s (1975, 1987, 1993) student academic and social integration model, Guiffrida’s (2003, 2004, 2005, 2006) model of relationships while at college, and ex-post facto research design, the study investigated personal and institutional factors that relate to Black students’ self-efficacy and persistence to the senior year in college. Data about Black ethnic undergraduate seniors’ (N = 236) academic and social experiences in college were collected using the Student Institutional Integration Survey (SIIS), an online questionnaire. Descriptive statistics were used to collect background information about the sample, correlation was calculated to indicate the degree of relationship between the variables, and multiple linear regressions were used to identify variables that are predictors of self-efficacy of persistence. Independent samples t-test and analyses of variance were computed to determine whether differences in perceptions of personal and institutional factors that relate to self-efficacy of persistence to the senior year in college could be identified between gender and ethnicity. Frequency was summarized to identify themes of participants’ primary motivation for finishing undergraduate degree programs. These themes were: (a) self-pride/personal goal, (b) professional aspiration/career (c) motivation to support family, (d) desire to have financial independence/better job, (e) to serve community, (f) opportunity to go to college, (g) being first-generation college student, and (h) prove to family the value of higher education. The research findings support the tenets of academic and social integration theories which suggest that students’ interaction with peer and faculty, relationships with family and friends, and involvement in institutional activities and organizations influence their persistence in college. Implications based on the findings affect institutional policy, curriculum, and program improvements that relate to Black undergraduate students’ academic and social support.