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.

Anarchy In The Airways

In his dialogue - Anarchy In The Airways - Joseph C. Von Kornfeld, Assistant Professor, College of Hotel Administration, University of Nevada, Las Vegas initially states: “Deregulation of the airline industry has brought about financial vulnerability for the traveling public. The author analyzes the situation since that point in time and makes recommendations for some solutions.” In this article, Assistant Professor Von Kornfeld, first defines the airline industry in its pre-regulated form. Then he goes into the ramifications and results of deregulating the industry, both in regards to the consumer, and in deregulation’s impact on the airlines themselves. “The most dramatic consequence of the pressures and turbulence of airline deregulation has been the unprecedented proliferation of airline bankruptcies,” Von Kornfeld informs. “Prior to the deregulation of the U.S. airline industry in 1978, U.S. air carriers operated in a business environment that was insulated from the normal stresses and strains of open competition. They were restricted from actively competing with fares and routings by the Civil Aeronautics Board (CAB),” Von Kornfeld says. In leveling the playing field, Von Kornfeld offers, “Each carrier was restricted to specific geographic routes, with those routes limited to two or three competing carriers. The only thing that set carriers apart in this CAB defined atmosphere was their ability to either advertise, or to enhance their level of service; or both. “…ultimately paid for by the passenger through fare increases sanctioned by the CAB,” Von Kornfeld states. “Airline service standards were unquestionably superior during the regulated environment,” Von Kornfeld renders an interesting observation. He does mention, however, that carrier safety was also considered a concern immediately prior to, and then after deregulation. “The major controversy focused on the allegation that safety and maintenance standards would be compromised due to the financial pressures brought about by an openly competitive environment,” Von Kornfeld says. Pricing, as well as labor unions are important factors in the equation, and Von Kornfeld addresses their relevance in the deregulated environment. “The primary rationalization for deregulation was to facilitate a more openly competitive environment. The increased competition was to ultimately have benefitted the consumer. Ironically, that’s not entirely the case, Von Kornfeld elaborates. In addressing some of the negative aspects of airline deregulation, Von Kornfeld suggests that some sort of federal re-regulation may be in order.