In this thesis we investigate whether a rank-one rotating mass matrix extended to solve the strong CP problem can, through the mass leakage mechanism, account for fermion masses, mixing angles and a $theta_{CP}$ term of order unity. In the first part we find restrictions placed on the rotation of the rank-one mass matrix by experimental data. We demonstrate that a smooth rotation of the mass matrix can reproduce the experimentally determined fermion masses and mixing angles and give $theta_{CP}$ = 1.45 radians. We then fit the speed of rotation at high ($> 1$ GeV) scales. Using this rotation we make predictions for Higgs branching ratios for a range of Higgs masses, finding a suppression of $Gamma(H ightarrow car{c})$ compared to the standard model and significant flavour violating branching ratios. In the second part we study the framed standard model (FSM). We calculate the strong framon one-loop contribution to the rotation of its rank-one mass matrix and account for the non-trivial metric on its internal symmetry space. We find that the FSM can reproduce the hierarchy seen in the fermion masses and the CKM matrix, fit $theta_{CP}sim0.3$ radians and find $|U_{mu3}|sim0.8$. Similar results are found if QCD running is included, except that $|U_{mu3}|>0.95$. We compare the FSM rotation to the rotation found in first part and find they are in good agreement above $mu=m_c$. We go on to show that the predictions for Higgs decay are comparable to those found in the general study. In the final part we calculate the framon mass spectrum of the FSM in the hermitian gauge and find that, as expected, it agrees with the calculation performed in the triangular gauge. We find that none of the framons are massless.

256 leaves : diags ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematical Physics, 1976

Dissipative time-dependent quantum transport theory with electron-phonon interaction in either weak or strong coupling regime is established. This theory goes beyond the conventional quantum master equation method and Kadanoff-Baym kinetic equations. It provides an efficient method for the simulation of transient quantum transport under arbitrary bias voltage with different electron-phonon coupling strength. First, time-dependent quantum transport theory for non-interacting system and its combination with first-principles method is developed. Based on the Padé expansion to Fermi function, and wide-band limit approximation of lead self-energy, a set of equations of motion is developed for efficient evaluation of density matrix and related quantities. To demonstrate its applicability, this method is employed to study the transient transport through a carbon nanotube based electronic device. Second, a dissipative time-dependent quantum transport theory is established in the weak electron-phonon coupling regime. In addition to the self-energy caused by leads, a new self-energy is introduced to characterize the dissipative effect induced by electron-phonon interaction. In the weak coupling regime, the lowest order expansion is employed for practical implementation. The corresponding closed set of equations of motion is derived, which provides an efficient and accurate treatment of transient quantum transport with electron-phonon interaction in the weak coupling regime. Numerical examples are demonstrated and its combination with first-principles method is also discussed. Next, a dissipative quantum transport theory for strong electron-phonon interaction is established by employing small polaron transformation. The corresponding equation of motions are developed, which is used to study the quantum interference effect and phonon-induced decoherence dynamics. Numerical studies demonstrate the formation of quantum interference effect caused by the transport electrons through two quasi-degenerate states with different couplings to the leads. The quantum interference can be suppressed by phonon scattering, which indicates the importance of considering electron-phonon interaction in these systems with prominent quantum interference effect when the electron-phonon coupling is strong. Last, the dissipative quantum transport theory for weak electron-phonon coupling regime is used to simulate the photovoltaic devices. Within the nonequilibrium Greens function formalism, a quantum mechanical method for nanostructured photovoltaic devices is presented. The method employs density-functional tight-binding theory for electronic structure, which make is possible to simulate the performance of photovoltaic devices without relying on empirical parameters. Numerical studies of silicon nanowirebased devices of realistic sizes with more than ten thousand atoms are performed and the results indicate that atomistic details and nonequilibrium conditions have clear impact on the photoresponse of the devices. / published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy

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258 leaves : appendix, offprints / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--Dept. of Mathematical Physics, University of Adelaide, 1973

The nonequilibrium Green’s function-hierarchical equation of motion (NEGFHEOM) method has been developed to simulate the time-dependent electron transport process. The real-time evolution of the reduced single-electron density matrix is solved through the Liouville-von-Neumann equation. The method is very efficient compared to conventional NEGF formulas which need to discretize the simulation time. The hierarchical equation of motion (HEOM) is closed at the second-tier in the time-dependent noninteracting Kohn-Sham framework. When combined with the wide band limit (WBL) approximation, the HEOM terminate at the first-tier. The resulting NEGF-HEOM-WBL method is particularly suitable for simulating the long time transient dynamics for large systems. The method developed is first applied to calculate the transient current through an array of as many as 1000 quantum dots. Upon switching on the bias voltage, the current increases linearly with respect to time before reaching its steady state value. And the time required for the current to reach its steady state value is exactly the time for a conducting electron to travel through the array at Fermi velocity. These phenomena can be understood by simple analysis on the energetics of the quantum dots or by classical electron gas model. Then the method is employed to investigate several simple molecular circuits, in which the para-linkage or meta-linkage benzene acts as the transmitting molecular entity. The simulation results shows that it takes a certain amount of time before the quantum interference manifests itself, and that the transmission through the meta case is hundreds of times smaller than that through the para case. To investigate the quantum interference process in molecular electronics, the concept of Büttiker probe is introduced. The Büttiker probe is an electrode that, when attached to electronic devices, causes the coherence passing through disappear. Simulation results show that the Büttiker probe can enhance the transmission of the meta benzene system through destroying the constructive interference. By turning the probe on and off, it can be observed that large strong correlations are indeed built up as electrons are transported through benzenoid structures - when the decoherence is turned off, the current rises, and when the decoherence is turned back on, the current falls. Finally, TDDFT(B)-NEGF-HEOM-WBL method is implemented to solve realistic systems in the formalism of time-dependent density functional theory (tightbinding). Ab initio calculations are carried out to simulate the time-dependent electron transport through a CNT-based device. The simulation results show that when the input bias voltage is in low frequency, both the conventional adiabatic approximation method and the NEGF-HEOM-WBL methods are good enough. However, when high frequency dynamic responses are need to be captured, the NEGF-HEOM-WBL method is more suitable. / published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy

A suitable subcategory of affine Azumaya algebras is defined and a functor from this category to the category of Zariski structures is constructed. The rudiments of a theory of presheaves of topological structures is developed and applied to construct examples of structures at a generic parameter. The category of equivariant algebras is defined and a first-order theory is associated to each object. For those theories satisfying a certain technical condition, uncountable categoricity and quantifier elimination results are established. Models are shown to be Zariski structures and a functor from the category of equivariant algebras to Zariski structures is constructed. The two functors obtained in the thesis are shown to agree on a nontrivial class of algebras.

For an arbitrary Nakajima quiver variety X, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the fundamental groupoid of a certain periodic locally finite hyperplane arrangement in Pic(X)⊗C. We identify the lattice part of this groupoid with the operators of quantum difference equation for X. The cases of quivers of finite and affine type are illustrated by explicit examples.

This thesis studies the Bar-Natan skein module of the solid torus with a particular boundary curve system, and in particular a diagrammatic presentation of it due to Russell. This module has deep connections to topology and categorification: it is isomorphic to both the total homology of the (n,n)-Springer variety and the 0th Hochschild homology of the Khovanov arc ring H^n. We can also view the Bar-Natan--Russell skein module from a representation-theoretic viewpoint as an extension of the Frenkel--Khovanov graphical description of the Lusztig dual canonical basis of the nth tensor power of the fundamental U_q(sl_2)-representation. One of our primary results is to extend a dualization construction of Khovanov using Jones--Wenzl projectors from the Lusztig basis to the Russell basis. We also construct and explore several deformations of the Russell skein module. One deformation is a quantum deformation that arises from embedding the Russell skein module in a space that obeys Kauffman--Lins diagrammatic relations. Our quantum version recovers the original Russell space when q is specialized to -1 and carries a natural braid group action that recovers the symmetric group action of Russell and Tymoczko. We also present an equivariant deformation that arises from replacing the TQFT algebra A used in the construction of the rings H^n by the equivariant homology of the two-sphere with the standard action of U(2) and taking the 0th Hochschild homology of the resulting deformed arc rings. We show that the equivariant deformation has the expected rank. Finally, we consider the Khovanov two-functor F from the category of tangles. We show that it induces a surjection from the space of cobordisms of planar (2m, 2n)-tangles to the space of (H^m, H^n)-bimodule homomorphisms and give an explicit description of the kernel. We use our result to introduce a new quotient of the Russell skein module.

Developments in the interdisciplinary field of quantum information open up previously impossible abilities in the realms of information processing and communication. Quantum entanglement has emerged as one property of quantum systems that acts as a resource for quantum information processing and, in particular, enables teleportation and secure cryptography. Therefore, the creation of entangled resources is of key importance for the application of these technologies. Despite a great deal of research the efficient creation of entanglement over long distances is limited by inevitable noise. This problem can be overcome by creating entanglement between nodes in a network and then performing operations to distribute the entanglement over a long distance. This thesis contributes to the field of entanglement distribution within such quantum networks. Entanglement distribution has been extensively studied for one-dimensional networks resulting in "quantum repeater" protocols. However, little work has been done on higher dimensional networks. In these networks a fundamentally different scaling, called "long distance entanglement distribution", can appear between the resources and the distance separating the systems to be entangled. I reveal protocols that enable long distance entanglement distribution for quantum networks composed of mixed state and give a few limitations to the capabilities of entanglement distribution. To aid in the implementation of all entanglement distribution protocols I finish by introducing a new system, composed of an optical nanofibre coupled to a carbon nanotube, that may enable new forms of photo-detectors and quantum memories.