The propsect of designing technologies around the quantum behavior of mesoscopic devices is enticing. This thesis present several tools to facilitate the process of calculating and analyzing the quantum properties of such devices – resonance, boundary conditions, and the quantum-classical correspondence are major themes that we study with these tools. In Chapter 1, we begin by laying the groundwork for the tools that follow by defining the Hamiltonian, the Green’s function, the scattering matrix, and the Landauer formalism for ballistic conduction. In Chapter 2, we present an efficient and easy-to-implement algorithm called the Outward Wave Algorithm, which calculates the conductance function and scattering density matrix when a system is coupled to an environment in a variety of geometries and contexts beyond the simple two-lead schematic. In Chapter 3, we present a unique geometry and numerical method called the Boundary Reflectin Matrix that allows us to calculate the full scattering matrix from arbitrary boundaries of a lattice system, and introduce the phenomenon of internal Bragg diffraction. In Chapter 4, we present a new method for visualizing wavefunctions called the Husimi map, which uses measurement by coherent states to form a bridge between the quantum flux operator and semiclassics. We extend the formalism from Chapter 4 to lattice systems in Chapter 5, and comment on our results in Chapter 3 and other work in the literature. These three tools – the Outward Wave Algorithm, the Boundary Reflection Matrix, and the Husimi map – work together to throw light on our interpretation of resonance and scattering in quantum systems, effectively codifying the expertise developed in semiclassics over the past few decades in an efficient and robust package. The data and images that they make available promise to help design better technologies based on quantum scattering. / Physics

published_or_final_version / Physics / Master / Master of Philosophy

In contemporary traffic flow theory, the distinction between user classes is rarely made. However, the accuracy and the descriptive power of the macroscopic traffic flow models can be improved significantly by separating user – classes and their specific flow characteristics. Additionally, the availability of a realistic multiple user – class traffic flow model enables the automated generation of user – dedicated traffic control policies by means of mathematical optimal control theory. A macroscopic multiple user – class model is derived from mesoscopic principles. In this paper there are analysed such a multiple user – class traffic flow model. Starting point for the analysis of the macroscopic flow model is the user – class specific phase – space density, which can be considered as a generalization of the traditional density. The gas – kinetic equations describing the dynamic of the multiclass Phase – Space Density (MUC - PSD) are governed by various interactions processes, such as accelerations towards a class – specific desired velocity, deceleration caused by vehicle interactions and the influence of lane changing. The gas – kinetic equations serve as the foundation of the proposed macroscopic traffic flow models, describing the dynamic of the class – dependent spatial density, velocity and velocity variance. These relations show competing processes: on the one hand, drivers accelerate towards their class – dependent desired velocity, while on the other hand, they need... [to full text]

Thesis (Ph.D.) -- McMaster University, 1997. / Includes bibliographical references (leaves 129-137). Also available via World Wide Web.

Thesis (M. Phil.)--University of Hong Kong, 2009. / Includes bibliographical references (leaves 74-75) Also available in print.

Thesis (Ph. D.)--University of Hong Kong, 2008.

Thesis (doctoral)--Technische Universiteit Delft, 1997. / Includes bibliographical references.

Thesis (M. Phil.)--University of Hong Kong, 1997. / Includes bibliographical references (leaves 62-65).

Thesis (Ph. D.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 162-164).

Thesis (Ph. D.)--University of Hong Kong, 1999. / Includes bibliographical references and index.