This thesis approaches questions concerning the thermalisation of subsystems of closed quantum systems, prepared in pure states of definite energy but far from equilibrium, under exact unitary evolution. Taking motivation from experiments in the field of ultracold atoms, an extensive study of relaxation to a thermal state in the Hubbard model is presented. The study of small local subsystems in Hubbard-model lattice clusters has led to some interesting findings. Explored are the effects of interactions between fermions, the initial-state energy and the energy uncertainty in the initial state and their effects on relaxation dynamics and thermalisation. The most significant finding is that while subsystem thermalisation is seen for a large range of subsystem-bath coupling strengths, the temporal form of the relaxation varies markedly from exponential decay for weak couplings with a crossover to Gaussian behaviour with increased coupling strength. This is found to hold more generally for random couplings between the subsystem and bath and for bosons as well as fermions, thus demonstrating generality. As well as being demonstrated numerically, this behaviour is derived for a generic class of bi-partite quantum systems which may be described with the use of random matrices. A Brownian motion model is employed to show the exponential to Gaussian crossover when the subsystem-bath coupling matrix takes a banded form. This result agrees well with numerical Hubbard-model results, and yields identical results at short times to those from straight-forward perturbative methods. It is demonstrated that the non-Markovian Gaussian behaviour should also be observable in the limit of macroscopic baths.

This thesis presents work undertaken with cold rubidium atoms interacting with an optical microcavity. The optical microcavity used is unique in its design, being formed between an optical fibre and silicon micromirror. This allows direct optical access to the cavity mode, whilst the use of microfabrication techniques in the design means that elements of the system are inherently scalable. In addition, the parameters of the system are such that a single atom has a substantial impact on the cavity field. In this system, two types of signal arise from the atoms' interaction with the cavity field; a `reflection' signal and a `fluorescence' signal. A theoretical description for these signals is presented, followed by experiments which characterise the signals under a variety of experimental conditions. The thesis then explores two areas: the use of the microcavity signals for atom detection and the investigation of how higher atom numbers and, as a result, a larger cooperative interaction between the atoms and the cavity field, impacts the signals. First, the use of these signals to detect an effective single atom and individual atoms whilst falling and trapped is explored. The effectiveness of detection is parameterised in terms of detection confidence and signal to noise ratio, detection fidelity and dynamic range. In the second part of this thesis, the effect of higher atom numbers on the reflection and fluorescence signals is investigated. A method for increasing the atom number is presented, alongside experiments investigating the impact on the measured signals. This is followed by experiments which explore the dispersive nature of the atom-cavity interaction by measuring the excitation spectrum of the system in reflection and fluorescence. In doing so, it is shown that, for weak coupling, these two signals are manifestly different.

Parallel flow in the scrape-off layer is a major area of interest in tokamak research, impacting on impurity transport, tritium retention and H-mode access. The work presented here is the first major investigation of SOL flow in the Mega Ampere Spherical Tokamak (MAST), using a Gundestrup probe specifically designed for the task. The results of a parameter scan in poloidal field, Bѳ, and temperature, T, of parallel velocity at the outboard mid-plane are presented, and the results and scalings compared to B2SOLPS5.0 simulations of MAST and a simple analytical model, in order to identify the relative importance of drift mechanisms (such as Pfirsch-Schluter and E × B) for driving parallel flow. The results show the predicted linear scaling with temperature and poloidal field strength, but also suggest a density dependence. Another major are of interest is the discovery in recent years of coherent filamentary structures that are radially convected through the L-mode SOL. These filaments are believed to contain sharp gradients in temperature, density and plasma potential, complicating probe analysis. An investigation to characterise the intermittency of the MAST SOL, it’s dependencies on poloidal field strength, density or temperature, and the impact of the filaments on probe measurements was also carried out, and a probe was built to further investigate the structure and dynamics of the filaments. Based on these experiments a method for resolving the flow in the filaments and background plasma was developed and applied in the flow experiments described above. It is found that the parallel Mach numbers are lower in the filaments than the ambient plasma in the far SOL — suggesting either ion temperatures are at least on the order of 4 times the electron temperature — or parallel flow velocity is substantially lower in the filaments than in the background plasma.

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The packing of molecules in solids greatly affects the properties of the bulk materials. This is particularly important for the pharmaceutical industry, where the discovery of crystal forms at a late stage of process development can have disastrous consequences. As a result, the importance of polymorphism in crystal structures of organic molecules has been recognised for many years. This thesis presents computational developments that can complement experimental form screening of molecules for which conformational flexibility is significant. Current methods for crystal structure prediction are limited by the extent of molecular flexibility that can be practically handled due to the prohibitive computational cost associated with quantum mechanical calculations integrated in most of the successful approaches. In order to reduce the number of quantum mechanical evaluations, local approximate models can be defined for the estimation of the intramolecular energy, molecular geometry and the conformationally dependent intermolecular electrostatic model. A novel algorithm, CrystalOptimizer, for the accurate local minimisation of the lattice energy of crystals involving flexible organic molecules is presented. The main novelty of the algorithm is the use of dynamically constructed and updated local approximate models which essentially make available the full accuracy of quantum mechanical models at each and every iteration of the minimisation algorithm, requiring only a small number of explicit quantum mechanical calculations. This has made possible the accurate treatment of molecules involving a relatively large numbers of atoms with significant flexibility in torsional and bond angles and even bond lengths. The performance of the algorithm is critically assessed and demonstrated on a set of single and multi-component crystals. An extension of an existing algorithm for the identification of low energy crystal structures of flexible molecules, CrystalPredictor, is also described. In the proposed modification, the intramolecular energy and the molecular conformation are modelled using local approximate models. This provides a more realistic model for the effects of the flexible degrees of freedom on the molecular geometry and lattice energy. The use of deterministic low-discrepancy sequences ensures an extensive and uniform coverage of the multivariable search space. A parallelised implementation of the algorithm allows minimisations from several hundreds of thousands of initial guesses to be carried out in reasonable time. A further computational benefit is derived by the storage of the information used to construct the local approximate models in databases, which can be re-used in subsequent re-minimisation of structures with more accurate models for the lattice energy. The usefulness of these modifications is demonstrated on the ROY molecule, for which the structures of all experimentally known polymorphs are identified by the algorithm. By combining the above algorithms, a comprehensive multi-stage methodology for ab initio determination of the crystal structure of a given molecule based solely on its atomic connectivity is presented. The application of the methodology to two large and flexible molecules of pharmaceutical interest is also demonstrated.

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