No description available.

The thesis falls in three chapters: (1) Spacetime; (2) Predictability; (3) Computability. The investigations are based on classical general relativity. So Chapter 1 provides a sketch of the background theory required for the following two chapters. Topics covered include: the Einstein field equations, causal structure, and handy hints on how to make new spacetimes from old. I also outline a simple singularity theorem and provide some statements of the cosmic censorship hypothesis. Chapter 2 begins by drawing a distinction between the notions of determinism and predictability. There follows a critique of Geroch's paper on relativistic prediction. A new definition of a predictable event is advanced, and some results regarding the global structure of spacetimes possessing such an event are given. Various apparently distinct generalisations of predictable spacetimes are considered and shown to be equivalent. Predictable spacetimes are sought among solutions to the Einstein field equations but not found. I create a worry that predictable spacetimes yield paradox; the worry is soothed. The connections with singularities are then investigated. Naked singularities are found to upset predictability, as expected. But the existence of predictable events is found to necessitate singularities, which is unexpected. Chapter 3 begins with Pitowsky's idea about how to perform a computation supertask in a relativistic spacetime. A fundamental flaw is corrected, and this leads to the definition of what is known as a <I>Malament-Hogarth</I> (M-H) spacetime. M-H spacetimes are shown to be non-globally hyperbolic, possess a non-compact slice, and to be prone to infinite blue-shifts. The rest of chapter is concerned with the bearing of M-H spacetimes on the concept of Computability. Membership of a recursively enumerable set is shown to be decidable by a single Turing machine (TM) operating in any M-H spacetime. A strict power hierarchy of other TM-based computers is shown to map precisely into the Kleene arithmetic hierarchy. Arithmetic is decidable by an even more powerful TM-based computer. There are radical implications for the concept of Computability; an analogy is found in the modern concept of Geometry.

In this thesis, the accuracy of model potentials developed for a variety of weakly bound systems is assessed. Stationary points on the potential energy surfaces are compared with ab initio results for both water and hydrogen fluoride clusters. The second pressure virial coefficient has also been calculated and compared with experimental data where available. The inclusion of quantum corrections, especially those associated with the rotational degrees of freedom, proves to be essential for an accurate description of this quantity. For small water clusters we have made a detailed comparison of many-body energies calculated using ab initio methods and two new model potentials. It is shown that induction energy is an important many-body term, so that two-body potentials which account for it correctly can be applied unchanged to many-body systems with good results. New models have been developed to study protonated water clusters and the validity of the rigid-body approximation is discussed. We show that the minimum energy structures are consistent with those located using density functional theory methods, and these are expected to compare well with correlated ab initio calculations. Here, the use of a model potential as a precursor to performing more accurate calculations has been demonstrated to be an economical way to proceed in the precise and systematic characterization of a system. The suitability of the Tang-Toennies damping functions commonly used to account for the short-range effects of charge-overlap on the dispersion energy has been examined. The argon dimer was chosen as a prototype system on which symmetry-adapted and intermolecular perturbation theory calculations were performed and compared. We show that such functions fit the data better when exchange as well as charge-overlap effects are considered. We also construct new damping functions and these provide a more accurate, yet still quite compact, description of the dispersion energy.

No description available.

No description available.

In the introductory chapter 1 review the hierarchy problem and some other unresolved issues in the Standard Model, and introduce the Minimal Supersymmetric Standard Model as a possible resolution of these issues. I review different mechanisms of supersymmetry breaking and examples from each class. I discuss the effects of superparticles on indirect Standard Model observables which will be used in the thesis, illustrating in particular the anomalous magnetic moment of the muon. The next part of the thesis examines the phenomenological implications of two models, Pure General Gauge Mediation and the Large Volume Scenario. I fit the models to low energy data and focus on the LHC and dark matter phenomenology, as well as issues of fine-tuning and the structure of the parameter space. In the final chapter I use indirect observables to calculate the Bayesian evidence for specific avatars of supersymmetry breaking from the introduction, using a statistical sampling technique. I discuss the prior dependence of the fits and the effects of the form of dark matter relic density constraint used. I quantify the constraining power and statistical pull of individual observables using the Kullback-Leibler divergence and present the constraints on the parameter space of the minimal anomaly and minimal gauge mediation models.

It is widely expected that over the next few years some evidence of low-energy super-symmetry (SUSY) will be found at collider experiments such as LHC, the Tevatron or a linear collider. This discovery would constitute a significant step in closing the current conceptual gap between experimental observations and proposed fundamental theories, which all make varying predictions about the mechanisms of SUSY breaking and the spectrum of resulting superparticles (sparticles). The focus of the search will therefore soon shift from the discovery of SUSY to more detailed studies of the proposed models of SUSY and SUSY breaking which would make it possible to select or rule out some models. Rather than analyzing the observable consequences of single points in the parameter space of SUSY breaking in detail, or reconstructing SUSY breaking parameters from low scale observables, I will present a procedure aiming to look at various models of SUSY breaking simultaneously. It does so by scanning over wide ranges of their input parameters to create an experimental footprint of each model in “measurement space”. The distance between these footprints gives a direct indication of the minimal set of measurements that is required to separate the models. This makes it possible to decide a priori whether two high scale models can be distinguished experimentally, and what measurement accuracy is necessary to do so. This procedure will be shown in a model scenario motivated by Type I string models. As soon as more than two dimensions are considered in the measurement space, it becomes impossible to obtain the spacing between the footprints by eye. Automatic techniques to judge the separation become necessary; a discussion of these, including the most promising one based on Genetic Algorithms, constitutes the latter part of this thesis.

We investigate discrete models for quantum gravity in three dimensions, based on topological quantum field theories. We begin by introducing the two main types of model which we shall investigate, namely Penrose's spin network model, and the Ponzano-Regge and Turaev-Viro simplicial state sum models. We briefly review the work of Ponzano and Regge showing how, in a certain semi-classical limit of their model, they cover three-dimensional Euclidean gravity. We go on to describe new work, by the author and J.W. Barrett, showing how the stationary points of a different semi-classical limit of the Ponzano-Regge partition function may be mapped to flat three-dimensional Lorentzian space, and consider how this partition function may be interpreted as a discrete version of a path integral for gravity in three dimensions. We describe the formalism of a topological quantum field theory. We examine the theory of Turaev and Viro, which is given by a simplicial state sum on a three-dimensional manifold, based on representations of the quantum group <I>U<SUB>q</SUB></I>(<I>sl</I>(2)). We show that it reduces to the Ponzano-Regge model in its <I>q</I> → 1 limit, and so it may be regarded as the naturally regularised version of that model. We describe new work investigating the relation between spin networks and simplicial state sum models. We show how the space of spin networks describes the state space for a two-dimensional surface in the Ponzano-Regge theory, and give a definition of the inner product on the state space which reproduces the topological inner product, defined by the union of two three-manifolds along their common boundary. We introduce Kauffman's <I>q</I>-deformed spin networks, and define the skein space, to which <I>q</I>-spin networks belong. We conjecture that a quotient of the skein space of a surface is isomorphic to the state space of the Turaev-Viro theory.

Carbon nanotubes and -fibres were selectively grown by chemical vapour deposition on pre-patterned catalysts. A systematic study was performed relating the growth and crystallinity of the carbon nanostructures to reactor characteristics, gaseous precursors and diluents as well as catalyst type and material. A DC plasma excitation at low discharge currents (<30 mA) not only resulted in vertical alignment of as-grown carbon nanofibres but, in combination with an acetylene feedback and nickel, cobalt or iron catalysts, enabled an onset of growth at temperatures below 300°C. Extended activation energies of 0.23 eV - 0.35 eV for the growth rate were much lower than for thermal growth (1.2 - 1.5 eV). This suggests a surface diffusion limited growth mechanism on a solid phase catalyst. The result allowed the direct synthesis of patterned, aligned carbon nanofibres onto polyimide foils to fabricate flexible field emitters. Carbon nanofibre-based scanning probes were achieved by novel catalyst patterning techniques, and complex shaped electrochemistry electrodes could be homogeneously covered with free-standing carbon nanofibres by using colloidal catalyst systems. The growth of silicon nanowires was studied based on silane as precursor gas and gold as thin film or colloidal catalyst. A low power RF (10 W) plasma significantly increased the growth rate at temperatures below 400°C. The as-grown silicon nanowires were highly crystalline with diameters (inner core <10 nm) small enough for the observation of quantum confinement effects. Element specific and general growth mechanisms of plasma enhanced chemical vapour deposition are highlighted.

In this dissertation, motivated both by our incomplete physical understanding, and by quantum information theory, we investigate quantum non-locality. In Chapter 2, we ask the question, which quantum states are non-local? We show that any entangled pure state is non-local, but that things are complicated with mixed states. In particular, following Werner’s local hidden variable model for projective measurements on a class of entangled states, we write down an extended model that works for arbitrary positive operator valued measurements performed by the separated observers. We also show that the existence of such a model for one particular quantum state implies the existence of a similar model for a wide class of other quantum states. Finally, we discuss the fact that some quantum states display a hidden non-locality, and describe a general classification scheme for the non-locality of quantum states. In Chapter 3, we turn to a particular protocol of quantum information theory, namely, quantum teleportation. We discuss the connections between quantum teleportation and non-locality. We drive a Bell-type inequality pertaining to the teleportation scenario and investigate when it is violated. We give an example of a situation in which a teleportation fidelity of ¾ is achieved without non-locality, even though this is greater than the classical limit of 2/3. In Chapter 4, we describe the experiments that have been performed as tests of quantum non-locality and the associated loopholes. We point out an assumption, the no-memory assumption that is common to nearly all analyses of Bell-type experiments, yet is not implied by locality. We remove the assumption and give a new analysis of the ideal case.