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.

The Acute Effects of Whole Body Vibration on Muscular Power and Agility

Context: While research suggests whole body vibration (WBV) positively affects measures of neuromuscular performance in athletes, researchers have yet to address appropriate and effective vibration protocols. Objective: To identify the acute effects of continuous and intermittent WBV on muscular power and agility in recreationally active females. Design: We used a randomized 3-period cross-over design to observe the effects of 3 vibration protocols on muscular power and agility. Setting: Sports Science and Medicine Research Laboratory at Florida International University. Patients or Other Participants: Eleven recreationally active female volunteers (age=24.4±5.7y; ht=166.0±10.3cm; mass=59.7±14.3kg). Interventions: Each session, subjects stood on the Galileo WBV platform (Orthometrix, White Plains, NY) and received one of three randomly assigned vibration protocols. Our independent variable was vibration length (continuous, intermittent, or no vibration). Main Outcome Measures: An investigator blinded to the vibration protocol measured muscular power and agility. We measured muscular power with heights of squat and countermovement jumps. We measured agility with the Illinois Agility Test. Results: Continuous WBV significantly increased SJ height from 97.9±7.6cm to 98.5±7.5cm (P=0.019, β=0.71, η2 =0.07) but not CMJ height [99.1±7.4cm pretest and 99.4±7.4cm posttest (P=0.167, β=0.27)] or agility [19.2±2.1s pretest and 19.0±2.1s posttest (P=0.232, β=0.21)]. Intermittent WBV significantly enhanced SJ height from 97.6±7.7cm to 98.5±7.7cm (P=0.017, β=0.71, η2 =0.11) and agility 19.4±2.2s to 19.0±2.1s (P=0.001, β=0.98, η2=0.16), but did not effect CMJ height [98.7±7.7cm pretest and 99.3±7.3cm posttest (P=0.058, β=0.49)]. Conclusion: Continuous WBV increased squat jump height, while intermittent vibration enhanced agility and squat jump height. Future research should continue investigating the effect of various vibration protocols on athletic performance.