published_or_final_version / Physics / Doctoral / Doctor of Philosophy

We numerically investigate electron transport properties in an electron waveguide which can be constructed in 2DEG of the heterostructure of GaAs and AlGaAs. We apply R-matrix theory to solve a Schrödinger equation and construct a S-matrix, and we then calculate conductance of an electron waveguide. We study single impurity scattering in a waveguide. A [delta]-function model as a single impurity is very attractive, but it has been known that [delta]-function potential does not give a convergent result in two or higher space dimensions. However, we find that it can be used as a single impurity in a waveguide with the truncation of the number of modes. We also compute conductance for a finite size impurity by using R-matrix theory. We propose an appropriate criteria for determining the cut-off mode for a [delta]-function impurity that reproduces the conductance of a waveguide when a finite impurity presents. We find quantum scattering echoes in a ripple waveguide. A ripple waveguide (or cavity) is widely used for quantum chaos studies because it is easy to control a particle's dynamics. Moreover we can obtain an exact expression of Hamiltonian matrix with for the waveguide using a simple coordinate transformation. Having an exact Hamiltonian matrix reduces computation time significantly. It saves a lot of computational needs. We identify three families of resonance which correspond to three different classical phase space structures. Quasi bound states of one of those resonances reside on a hetero-clinic tangle formed by unstable manifolds and stable manifolds in the phase space of a corresponding classical system. Resonances due to these states appear in the conductance in a nearly periodic manner as a function of energy. Period from energy frequency gives a good agreement with a prediction of the classical theory. We also demonstrate wavepacket dynamics in a ripple waveguide. We find quantum echoes in the transmitted probability of a wavepacket. The period of echoes also agrees with the classical predictions. We also compute the electron transmission probability through a multi-ripple electron waveguide. We find an effect analogous to the Dicke effect in the multi-ripple electron waveguide. We show that one of the S-matrix poles, that of the super-radiant resonance state, withdraws further from the real axis as each ripple is added. The lifetime of the super-radiant state, for N quantum dots, decreases as [1/N] . This behavior of the lifetime of the super-radiant state is a signature of the Dicke effect. / text

We numerically investigate a total transmission probability through QDs embedded in an AB ring. The QDs are formed by delta function-like double potential barriers and a magnetic flux is penetrated in the center of the ring. In particular, we study the coupled double-QDs in series and non-coupled double-QDs in parallel in an AB ring. In each model, we show the total transmission probability as a function of QD size and electron incident energy, and present the transmission amplitude on the complex-energy plane. Of interest is the change and progression of Fano resonances and corresponding zero-pole pairs on the complex-energy plane with magnetic flux in the center of the ring.To accomplish this, we analytically solve the scattering matrix at each junction and the transfer matrix through the arms of the ring using Schrodinger equation for the delta function barriers. Then, the total transmission probability is obtained as a function of electron energy and magnetic flux by cascading these matrices. Finally, the solutions of the analytical equations and the graphical output of the transmission characteristics in the system will be obtained numerically by using Mathematica programs run on desktop computers. / Department of Physics and Astronomy