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. ^

Simulating everglades national park hydrology and phosphorus transport under existing and future scenarios using numerical modeling

The Florida Everglades has a long history of anthropogenic changes which have impacted the quantity and quality of water entering the system. Since the construction of Tamiami Trail in the 1920's, overland flow to the Florida Everglades has decreased significantly, impacting ecosystems from the wetlands to the estuary. The MIKE Marsh Model of Everglades National Park (M3ENP) is a numerical model, which simulates Everglades National Park (ENP) hydrology using MIKE SHE/MIKE 11software. This model has been developed to determine the parameters that effect Everglades hydrology and understand the impact of specific flow changes on the hydrology of the system. ^ As part of the effort to return flows to the historical levels, several changes to the existing water management infrastructure have been implemented or are in the design phase. Bridge construction scenarios were programed into the M3ENP model to review the effect of these structural changes and evaluate the potential impacts on water levels and hydroperiods in the receiving Northeast Shark Slough ecosystem. These scenarios have shown critical water level increases in an area which has been in decline due to low water levels. Results from this work may help guide future decisions for restoration designs. ^ Excess phosphorus entering Everglades National Park in South Florida may promote the growth of more phosphorus-opportunistic species and alter the food chain from the bottom up. Two phosphorus transport methods were developed into the M3ENP hydrodynamic model to determine the factors affecting phosphorus transport and the impact of bridge construction on water quality. Results showed that while phosphorus concentrations in surface waters decreased overall, some areas within ENP interior may experience an increase in phosphorus loading which the addition of bridges to Tamiami Trail. Finally, phosphorus data and modeled water level data was used to evaluate the spectral response of Everglades vegetation to increasing phosphorus availability using Landsat imagery.^

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.

Simulating Everglades National Park hydrology and phosphorus transport under existing and future scenarios using numerical modeling

The Florida Everglades has a long history of anthropogenic changes which have impacted the quantity and quality of water entering the system. Since the construction of Tamiami Trail in the 1920's, overland flow to the Florida Everglades has decreased significantly, impacting ecosystems from the wetlands to the estuary. The MIKE Marsh Model of Everglades National Park (M3ENP) is a numerical model, which simulates Everglades National Park (ENP) hydrology using MIKE SHE/MIKE 11software. This model has been developed to determine the parameters that effect Everglades hydrology and understand the impact of specific flow changes on the hydrology of the system. As part of the effort to return flows to the historical levels, several changes to the existing water management infrastructure have been implemented or are in the design phase. Bridge construction scenarios were programed into the M3ENP model to review the effect of these structural changes and evaluate the potential impacts on water levels and hydroperiods in the receiving Northeast Shark Slough ecosystem. These scenarios have shown critical water level increases in an area which has been in decline due to low water levels. Results from this work may help guide future decisions for restoration designs. Excess phosphorus entering Everglades National Park in South Florida may promote the growth of more phosphorus-opportunistic species and alter the food chain from the bottom up. Two phosphorus transport methods were developed into the M3ENP hydrodynamic model to determine the factors affecting phosphorus transport and the impact of bridge construction on water quality. Results showed that while phosphorus concentrations in surface waters decreased overall, some areas within ENP interior may experience an increase in phosphorus loading which the addition of bridges to Tamiami Trail. Finally, phosphorus data and modeled water level data was used to evaluate the spectral response of Everglades vegetation to increasing phosphorus availability using Landsat imagery.