<p>In this thesis only Binary codes are studied. Firstly, the codes overs the field GF(2) by the adjacency matrix of the complement T(n), ofthe triangular graph, are examined. It is shown that the code obtained is the full space F2 s(n/2) when n= 0 (mod 4) and the dual code of the space generated by the j-vector when n= 2(mod 4). The codes from the other two cases are less trivial: when n=1 (mod 4) the code is [(n 2), (n 2 ) - n + 1, 3] code, and when n = 3 (mod 4) it is an [(n 2), (n 2) - n, 4 ] code.</p>

<p> The kinematics and dynamics for plane wave optics are derived for a massive electrodynamic field by utilizing Proca's theory. Atomic spectroscopy is also examined, with the focus on the 21 cm radiation due to the hyperfine structure of hydrogen. The modifications to Snell's Law, the Fresnel formulas, and the 21 cm radiation are shown to reduce to the familiar expressions in the limit of zero photon mass.</p>

The motivation for this Masters thesis is to develop numerical algorithms to study the dynamical evolution of non-Markovian open quantum systems. Such systems are of importance if one is interested in modeling solid state systems which are candidates for the qubit - the quantum analog of the binary digit. Such an example may be a trapped spin onto which is encoded a chosen spin state. In reality, such a spin is never completely isolated from the environment, and so from a practical point of view it is of interest to study the dynamics of this interaction between some open system with an environment. The goal here is to create a computer program to simulate this behaviour of all density matrix elements for the open system numerically. Many interesting quantum systems, spin chains as an example, do not behave as a Markovian process, and it is sometimes difficult or perhaps indeed impossible to derive exact analytical solutions. As such, the techniques used in this thesis are aimed at describing non-Markovian processes in a way that approaches the exact solution. The study begins by introducing the reader to important concepts and results in the general study of both closed and open quantum systems. Differences in the treatment of the two types of systems are pointed out, and the necessary standard equations used generally are presented. Additionally, two different techniques are explained for the study of open quantum systems, namely the density matrix approach and the stochastic wavefunction approach. Important results from these two methods are presented and the section ends by convincing the reader of their equivalence. The second chapter begins with an example of an open quantum system which exhibits non-Markovian behaviour. The model of the spin star system is described and important results are given from references. This chapter introduces the reader to the model, conceptually explaining the system, and going on to show its exact analytical behaviour. This basic model, with minor changes, will be used throughout this study and the physics, interactions and symmetries, does not really change. This study then shows how one can use the stochastic wavefunction method to solve the dynamics of the spin star model. This chapter follows with deriving stochastic equations for the same system as the preceding chapter, and using these equations a numerical algorithm is developed, the results of which provide a good comparison between the exact analytical and exact numerical techniques. As a further example, a similar but slightly more complex system is studied in exactly the same manner, with the only important difference being that the open quantum system to be modeled is now a spin-one particle. Important differences in the results are pointed out and explained, and important similarities are highlighted. In presenting the results of this second simulation, shortcomings of the numerical technique and areas of applicability are discussed. In the final chapter the author considers using this numerical technique's ability to completely map the dynamics for a density matrix to investigate a measure of quantumness for an open system. This research has been submitted for publication to a peer reviewed journal. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2007.

<p> In this dissertation, scenarios where strong conformal dynamics constitutes the ultraviolet completion of the physics that drives electroweak symmetry breaking are considered. It is shown that in theories where the operator responsible for the breaking of conformal symmetry is close to marginal at the breaking scale, the dilaton mass can naturally lie below the scale of the strong dynamics. However, in general this condition is not satisfied in the scenarios of interest for electroweak symmetry breaking, and so the presence of a light dilaton in these theories is associated with mild tuning. The effective theory of the light dilaton is constructed in this framework, and the form of its couplings to Standard Model states are determined. It is shown that corrections to the form of the dilaton interactions arising from conformal symmetry violating effects are suppressed by the square of the ratio of the dilaton mass to the strong coupling scale, and are under good theoretical control. These corrections are generally subleading, except in the case of dilaton couplings to marginal operators, when symmetry violating effects can sometimes dominate. Phenomenological implications of these results are investigated for models of technicolor, and for models of the Higgs as a pseudo-Nambu-Goldstone boson, that involve strong conformal dynamics in the ultraviolet.</p><p> Using AdS/CFT correspondence, a holographic realization of this scenario is obtained by constructing the effective theory of the graviscalar radion in the Randall-Sundrum models, taking stabilization into account. The conditions under which the radion can remain light are explored, and the corrections to its couplings to Standard Model (SM) states localized on the visible brane are determined. It is shown that in the theories of interest for electroweak symmetry breaking that have a holographic dual, the presence of a light radion requires mild tuning. Corrections to the form of the radion coupling to SM states arising from effects associated with brane stabilization are also calculated. These corrections scale as the square of the ratio of the radion mass to the Kaluza-Klein scale, and are generally subleading, except in the case of gluons and photon, when they can sometimes dominate. These results are in agreement with and lend robustness to the conclusions for the dilaton.</p>

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