Studies On The Simulation Of Quantum Transport And Quantum Chaos In Mesoscopic Systems

Semiconductor devices are downsizing due to the rapid advancements in semiconductor technology. It has reached the mesoscopic scale nowadays but rather than the macro scale. The study of the quantum transport in mesoscopic system becomes then very important. Furthermore, phenomena of the quantum chaos has been found by such a study. Investigations on the quantum transport and the quantum chaos in mesoscopic system are helpful to the further development of semiconductor technology. This thesis, based on the research results that have already been achieved in past, studies numerically the quantum transport and the quantum chaos in mesoscopic system. It consists of the following six chapters.In Chapter One, the basic concepts of mesoscopic system are introduced. It is explained the Landauer-Büttiker formalism for calculating the conductance and the scattering matrix method for calculating the transmission coefficient. In addition, the researches on ballistic phonon and the thermal conductance are reviewed. The scarring wave function, a kind of quantum behavior in classical chaotic systems, is introduced; the study of quantum scarring in mesoscopic system is reviewed.In Chapter Two, by using the scattering matrix method, we investigate the transmission coefficient of acoustic phonon and the thermal conductance in a double-bend waveguide structure. The calculation results show that, the transmission coefficients have strong resonances due to scattering in the midsection of a double-bend structure; the position and the width of the resonance peaks are determined by the dimensions of the midsection of a structure. Due to such scattering of phonon the thermal conductance decreases with the increasing of the temperature first, then increases after reaches a minimum. Furthermore, the investigation on the multiple double-bend structures in series indicates that, the first additional double-bend structure suppresses the transmission coefficient and forms then the frequency gap; further additional double-bend structures have no effect on the gap position and width, but can increase the number of the resonance peaks at the frequency just above the gap region.In Chapter Three, by using the method with SU(2) partially coherent states, we analytically study the influences of the probe perturbation on the scarred wave function in a 2D open square billiard by treating the probe perturbation as a δ-function type impurity. The calculated probability densities agree well with the experimental results reported. The calculation...