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.

A Multi-Criteria GIS-Based Route Selection Tool for Hazardous Material Transport: Consideration of Environmental Consequence, Traffic Congestions and Costs

Hazardous materials are substances that, if not regulated, can pose a threat to human populations and their environmental health, safety or property when transported in commerce. About 1.5 million tons of hazardous material shipments are transported by truck in the US annually, with a steady increase of approximately 5% per year. The objective of this study was to develop a routing tool for hazardous material transport in order to facilitate reduced environmental impacts and less transportation difficulties, yet would also find paths that were still compelling for the shipping carriers as a matter of trucking cost. The study started with identification of inhalation hazard impact zones and explosion protective areas around the location of hypothetical hazardous material releases, considering different parameters (i.e., chemicals characteristics, release quantities, atmospheric condition, etc.). Results showed that depending on the quantity of release, chemical, and atmospheric stability (a function of wind speed, meteorology, sky cover, time and location of accidents, etc.) the consequence of these incidents can differ. The study was extended by selection of other evaluation criteria for further investigation because health risk as an evaluation criterion would not be the only concern in selection of routes. Transportation difficulties (i.e., road blockage and congestion) were incorporated as important factor due to their indirect impact/cost on the users of transportation networks. Trucking costs were also considered as one of the primary criteria in selection of hazardous material paths; otherwise the suggested routes would have not been convincing for the shipping companies. The last but not least criterion was proximity of public places to the routes. The approach evolved from a simple framework to a complicated and efficient GIS-based tool able to investigate transportation networks of any given study area, and capable of generating best routing options for cargos. The suggested tool uses a multi-criteria-decision-making method, which considers the priorities of the decision makers in choosing the cargo routes. Comparison of the routing options based on each criterion and also the overall suitableness of the path in regards to all the criteria (using a multi-criteria-decision-making method) showed that using similar tools as the one proposed by this study can provide decision makers insights in the area of hazardous material transport. This tool shows the probable consequences of considering each path in a very easily understandable way; in the formats of maps and tables, which makes the tradeoffs of costs and risks considerably simpler, as in some cases slightly compromising on trucking cost may drastically decrease the probable health risk and/or traffic difficulties. This will not only be rewarding to the community by making cities safer places to live, but also can be beneficial to shipping companies by allowing them to advertise as environmental friendly conveyors.