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A phenomenolgical analysis of t-m body scattering data with particular emphasis on the phase and energy dependence overegged cut corrections is presented. After a brief summary of the Regge philosophy and approach, we survey the experimental data in chapter two. We note that all hadronic processes, as distinct from photoproduction appear to exhibit strong Regge shrinkage at large |t|. In chapter three, we motivate the eikonal model approach and show how it is used to calculate cuts in π N charge exchange and in photoproduction. Most of the phase problems encountered in the naive absorption models can be overcome, provided we use the true elastic amplitude (which we represent as a sum of P + P’ poles) to generate the absorptive corrections. We conclude this chapter by discussing how the shrinkage of the eikonal model cuts is inconsistent with the α(_eff)’s of chapter two for hadronic processes. We digress a little in chapter four to examine the important role played by t-channel unitarity and show how it can solve some of the problems outlined in the previous chapter by peaking the cut discontinuity at the position of the pole. Finally, we propose a new scheme for calculating Regge cuts and in the last chapter construct a specific model for π N CEX and π º photoproduction. A detailed examination of the cut discountinuity provides a possible explanation for the different energy dependence of these ostensibly similar processes. In conclusion, we discuss the implications of our model for the traditional (Michigan and Argonne) approaches to Regge cut phenomenology and suggest some areas which may provide interesting tests of the model.

The object of this thesis is twofold. The first part concerns the improvement of the unitary operator of Buccella et al. This operator is an example of a Melosh transformation connecting the algebras of the constituent and current quarks. The second part of this thesis examines the structure of the multiplets and the corresponding Lagrangians arising from the enlarged supersymmetry algebra incorporating isospin. Chapter One is a general introduction to the Melosh transformation and the work done by Buccella et al. The second chapter examines the difficulties involved with the Buccella transformation and contains a discussion on its possible improvement. In the third and final chapter on the Buccella transformation these improvements are implemented successfully, giving a unitary transformation which is correct to the second order of a perturbation expansion. Using this transformation we are able to obtain mass equations which are in good agreement with experiment in addition to the usual successful predictions for axial couplings typical of Melosh transformations in general. Chapter Four gives a general introduction to the concept of supersymmetry, describing the successes of the original model and also its special points of interest. The fifth chapter looks in detail at the structure of the multiplets arising from the larger super-algebra incorporating isospin, suggested by Salam and Strathdee. In the sixth chapter we try to form "super-invariant" Lagrangian densities from these multiplets which are physically applicable. Finally there is a discussion of our conclusions.

This thesis deals with some general work on the ND(^-1) equations and, more specifically, with two calculations which make use of them. Chapter 1 commences with a brief outline of the subject, followed by a fairly detailed analysis of numerical methods of solution of the equations, including an analysis of cut off and threshold problems. In particular we demonstrate a particular form of numerical solution which appears to be rather superior to any previous ones. Chapter 2 discusses the problems that arise when a multi-channel calculation is approximated to be a single channel one: we show that in general the results are different, and discuss the conditions for them to agree. Chapter 3 investigates what happens when N and D have simultaneous zeroes: it is shown that a potential that leads to this is necessarily singular and repulsive. Chapter 4 opens with a general review of the successes and failures of the quark model in scattering theory. It is shown that the quark model is necessarily inconsistent with what is commonly called bootstrap philosophy, and we investigate whether a reasonably convincing quark model may be constructed. Chapter 5 outlines a calculation of the πN P(_11) phase shift. The previous work on this problem is discussed, and the computational method is outlined along with a discussion of what results can be expected from the calculation.

In this thesis, we are concerned with models of explicit wavefunction collapse as a possible solution to the measurement problem of quantum mechanics. We examine the models where collapse is to near-position eigenstates, originally introduced by Ghirardi, Rimini and Weber in 1986, where the wavefunction is spontaneously localized at random times. Subsequent models where some of the problems of the GRW model are solved, are discussed, for both sudden localization and continuous localization processes. We comment briefly on the possible origins of collapse. The consequences of possible wavefunction collapse on the operation of quantum computers are described. Finally, we look at an attempt to describe the collapse process in a Lorentz-invariant manner.

In this thesis we shall present work concerning the description of the emergence of solitonic fundamental strings from stable, finite energy, compact D3-branes in a subspace of $AdS_{5}\times S^{5}$ and their subsequent interaction. We work in the planar limit and focus on states of large angular momentum $J$ corresponding to large R-charge in the dual gauge theory. We begin by constructing the full set of boundary giant magnons on $\mathbb{R}\times S^{2}$ attached to the maximal $Z=0$ giant graviton by mapping from the general solution to static sine-Gordon theory on the interval. We then compute the values of the anomalous dimension, $\Delta-J$, of the dual gauge theory operators at finite $J$, examining the behaviour of the leading order corrections when $J$ is large. We then consider the Born-Infeld theory of the giant graviton itself coupled to the background 5-form flux. Constructing BIon spike solutions that correspond to the world volume description of the boundary giant magnons we find a limit amenable to analysis which returns the full range of behaviour exhibited at finite $J$. Finally we produce the open strings on $\mathbb{R}\times S^{2}$ that correspond to the solutions of integrable boundary sine-Gordon theory. Relating the boundary parameters in a way that ensures a given set of string boundary conditions we describe the scattering of giant magnons with non-maximal $Y=0$ giant gravitons and calculate the leading contribution to the associated magnon scattering phase. Our method necessarily describes all integrable scatterings of giant magnons with giant gravitons.

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In this Thesis we study steady state solutions and dynamical evolutions of two– component atomic Bose–Einstein Condensates. We initially investigate the equilibrium properties of condensate mixtures in harmonic trapping potentials at zero temperature. Subsequently we simulate the coupled growth of these condensates by inclusion of damping terms. Finally, we investigate the evolution of coupled Bose gases via the so-called classical–field method. A recent experiment [D. J. McCarron et al., Phys. Rev. A, 84, 011603(R) (2011)] achieved Bose–Einstein Condensation of a two–species 87Rb–133Cs phase segregated mixture in harmonic trapping potentials. Depending on relative atom numbers of the two species, three distinct regimes of density distributions were observed. For these experimental parameters, we investigate the corresponding time–independent ground state solutions through numerical simulations of the coupled Gross–Pitaevskii equations. By including experimentally relevant shifts between the traps, we observe a range of structures including ‘ball and shell’ formations and axially/radially separated states. These are found to be very sensitive to the trap shifts. For all three experimental regimes, our numerical simulations reveal good qualitative agreement. The observed experimental profiles cannot be guaranteed to be fully equilibrated. This, coupled with the rapid sympathetic cooling of the experimental system, leads to a situation where growth may play a determining factor in the density structures formed. To investigate this further, we introduce phenomenological damping to describe the associated condensate growth/decay, revealing a range of transient structures. However, such a model always predicts the predominance of one condensate species over longer evolution times. Work undertaken by collaborators with the more elaborate Stochastic Projected Gross–Pitaevskii equations, which can describe condensate formation by coupling to a heat bath, predicts the spontaneous formation of dark–bright solitons. Motivated by this, we show how the presence of solitons can affect the condensate distribution, thus highlighting the overall dynamical role in the emerging patterns. Finally, we use classical field methods to analyse the evolution of non trapped Bose gases from strongly nonequilibrium initial distributions. The contrast between miscible (overlapping) and immiscible (phase segregated) components gives rise to important distinctions for condensate fractions and the formation of domains and vortices. In addition, splitting the particles of a single component thermalised state into two components is investigated. We then study the effects of suddenly quenching the strength of the interspecies interactions. Under suitable conditions, this quench generates isotropic vortex tangles. While this tangle subsequently decays over time, we propose how a repeat sequence of quenches at regular intervals could be employed to drive the tangle, thereby potentially providing a novel route to the generation of quantum turbulence.

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