| In the past two decades, significant progress in constructing physical systems of reduced dimensionality has been made. In these systems, quantum effects are observed in the electric current response to an applied bias voltage. Considerable theoretical effort has been made to understand conductance and capacitance which characterize this response. In addition to a fundamental science interest, there has been a significant technological need to build and understand small scale devices in order to maintain the current rate of progress in increasing computer performance.; In this thesis, we theoretically investigated the conductance and capacitance of mesoscopic and molecular scale systems. Our approach incorporated Landauer-Buttiker transport theory.; We developed a highly efficient method, based on the solution of the time-dependent Schrodinger equation incorporating a magnetic field, to solve the quantum scattering problem in mesoscopic nanostructures. We studied linear response capacitance in a two plate mesoscopic capacitor with one plate a quantum conductor in the ballistic scattering regime. By determining the scattering wavefunctions in the quantum plate, we were able to obtain relevant densities of states and use them to self-consistently calculate capacitance matrix coefficients for the system. We find the capacitance to be highly dependent on the external magnetic field and the number of probes attached to the quantum conductor.; To study molecular scale systems, our approach was based on Density Functional Theory within Local Density Approximation and non-equilibrium Green's functions, implemented in the simulation package McDcal. For the work in this thesis, we modified McDcal to run on parallel computer architectures. We studied the current-voltage characteristics of silicon cage nanowires sandwiched between aluminum electrodes. We successfully analyzed our results using the complex band structure of the nanowire. Finally, we studied the capacitance properties of carbon nanotube junctions. In junctions with tubes so far apart that their wavefunctions do not overlap, we studied the variation in capacitance for different relative tube positions and radii. We also studied junctions where the nanotubes are in contact but in which there is no current due to a conductance gap. In this system we find an enhancement in the value of capacitance. |
