The spin-dynamics of Fermi-liquid helium-3 in pure form and in its mixtures with helium-4 are considered in this thesis. A linearised model of the spin dynamics is developed from Leggett's equation of motion, including spin-diffusion, the Leggett-Rice spin-rotation effect and cylindrical boundary conditions . The equations are solved using a matrix formalism, allowing simulation of FIDs, NMR spectra and spin-echoes. The boundary conditions are shown to cause deviations of spin-echo amplitude and phase from the predictions of Leggett and Rice, for realistic experiments. The model is extended to include the demagnetising field (dipolar field) due to the magnetisation of the sample itself. Simulations show that, when the demagnetising field is strong, spectral clustering is present and sharp peaks are observed in the NMR spectrum. Data from NMR experiments on 3He and 3He-4He mixtures in an 11.3T magnetic field, performed in Nottingham in 1999/2000, are analysed. The analysis of 6.2% 3He mixture is predominantly by least-squares fitting of the model (excluding demagnetising field) to spin-echo data, yielding the transverse spin-diffusion coefficient and spin-rotation parameter as functions of temperature down to 3.4mK. Parameters are seen to deviate from the 1/Ta^2 characteristic of Fermi-liquid transport parameters, with a 1/(T^2+Ta^2) form, indicative of spin-transport anisotropy. The anisotropy temperature scale Ta is found to be 6+-1 mK. Analysis of pure 3He experiments is by qualitative comparison of spectroscopic data with the model (including demagnetising field): many observed features are reproduced by the simulation.

An extremely wide variety of self-organised nanostructured patterns can be produced by spin-casting solutions of colloidal nanoparticles onto solid substrates. This is an experimental regime that is extremely far from thermodynamic equilibrium, due to the rapidity with which the solvent evaporates. It is the dynamics of flow and evaporation that lead to the formation of the complex structures that are observed by atomic force microscopy (AFM). The mechanisms involved in the formation of these patterns are not yet fully understood, largely because it is somewhat challenging to directly observe the evaporation dynamics during spin-casting. Monte Carlo simulations based on a modified version of the model of Rabani et al. [1] have allowed the study of the processes that lead to the production of particular nanoparticle morphologies. Morphological image analysis (MIA) techniques are applied to compare simulated and experimental structures, revealing a high degree of correspondence. Furthermore, these tools provide an insight into the level of order in these systems, and improve understanding of how a pattern’s specific morphology arises from its formation mechanisms. Modifying the properties of a substrate on the scale of a few hundred nanometres by AFM lithography has a profound effect on the processes of nanoparticle pattern formation. The simulation model of Rabani et al. was successfully modified to account for the effect of surface modification. The simulations were further modified to reproduce cellular structures on two distinct length scales– a phenomenon that is commonly seen in experiments. The dynamic behaviour of simulated nanoparticle structures is examined in the “scaling” regime in relation to recent experiments carried out by Blunt et al. [2] in an attempt to understand the coarsening mechanism. Finally, a genetic algorithm approach is applied to evolve the simulations to a target morphology. In this way, an experimental target image can be automatically analysed with MIA techniques and compared with an evolving population of simulations until a target “fitness” is reached.

In this thesis, we describe, both semiclassically and quantum mechanically, the single-particle and collective dynamics of electrons and ultracold atoms moving through periodic potentials. Firstly, we explore collective electron dynamics in superlattices with an applied voltage and tilted magnetic field. Single electrons in this system exhibit non-KAM chaotic dynamics. Consequently, at critical field values, coupling between Bloch and cyclotron motion causes delocalisation of the electron orbits, resulting in strong resonant enhancement of the drift velocity. We show that this dramatically affects the collective electron behaviour by inducing multiple propagating charge domains and, consequently, GHz-THz current oscillations with frequencies ten times higher than with no tilted field. Secondly, we study the effect of applying an acoustic wave to the superlattice and find that we can induce high-frequency single electron dynamics that depend critically on the wave amplitude. There are two dynamical regimes depending on the wave amplitude and the electron's initial position in the acoustic wave. Either the electron can be dragged through the superlattice and is allowed to perform drifting periodic orbits with THz frequencies far above the GHz frequencies of the acoustic wave; or, by exerting a large enough potential amplitude, Bloch-like oscillations can be induced, which can cause ultra-high negative differential velocity. We also consider collective electron effects and find that, generally, the acoustic wave drags electrons through the lattice. Additionally, high negative differential drift velocity at the transition between these two single-electron dynamical regimes, induces charge domains in the superlattice that generates extra features in the current oscillations. Finally, we investigate cold atoms in optical lattices driven by a moving potential wave, directly analogous to acoustically-driven superlattices. In this case, we find the same dynamical regimes found in the acoustically driven superlattice. In addition, there are a number a sharp resonant features in the velocity of the atom at critical wave amplitudes and speeds. This could provide a flexible mechanism for transporting atoms to precise locations in a lattice.

In this thesis, the sensitivity of a range of plasmonic gold nanostructures to changes in ambient electric potential has been studied using a high quality objective-type dark-field imaging spectrometer, which was capable of measuring the signal from single nanoparticles. Optical response of the nanostructure to the change of physiologically relevant potential has been investigated experimentally and theoretically. Simulations to predict the sensitivity to potential changes were in good qualitative agreement with experimental data. The similar transients of scattering produced by potential cyclic voltammetry and potential step for gold film and gold nanoprism indicated that the mechanism of potential perturbation on the gold nanostructures was independent of their morphologies. The relationship between the morphologies of the gold nanostructure and their ability for voltage sensing had been investigated in detail. The cost-effective ultrathin gold film provides the highest voltage sensitivity and appears to be extremely promising as the basis for the design of an ultrasensitive plasmonic nanostructure sensor for electrical signals.

Bose-Einstein condensates (BECs) have been one of the most active areas of research since their experimental birth in 1995. The complicated nature of the experiments on BECs suggests to observe them in reduced dimensions. The dependence of the collective excitations of the systems on the spatial degrees of freedom allows the study in lower dimensions. In this thesis, we first study two effectively one-dimensional parallel linearly coupled BECs in the presence of external potentials. The system is modelled by linearly coupled Gross-Pitaevskii (GP) equations. In particular, we discuss the dark solitary waves and the grey-soliton-like solutions representing analogues of superconducting Josephson fluxons which we refer to as the fluxon analogue (FA) solutions. We analyze the existence, stability and time dynamics of FA solutions and coupled dark solitons in the presence of a harmonic trap. We observe that the presence of the harmonic trap destabilizes the FA solutions. However, stabilization is possible by controlling the effective linear coupling between the condensates. We also derive theoretical approximations based on variational formulations to study the dynamics of the solutions semi-analytically. We then study multiple FA solutions and coupled dark solitons in the same settings. We examine the effects of trapping strength on the existence and stability of the localized solutions. We also consider the interactions of multiple FA solutions as well as coupled dark solitons. In addition, we determine the oscillation frequencies of the prototypical structures of two and three FA solutions using a variational approach. Finally, we consider two effectively two-dimensional parallel coupled BECs enclosed in a double well potential. The system is modelled by two GP equations coupled by linear and nonlinear cross-phase-modulations. We study a large set of radially symmetric nonlinear solutions of the system in the focusing and defocusing cases. The relevant three principal branches, i.e. the ground state and the first two excited states, are continued as a function of either linear or nonlinear couplings. We investigate the linear stability and time evolution of these solutions in the absence and presence of a topological charge. We notice that only the chargeless or charged ground states can be stabilized by adjusting the linear or nonlinear coupling between the condensates.

A central aim of the field of relativistic quantum information (RQI) is the investigation of quantum information tasks and resources taking into account the relativistic aspects of nature. More precisely, it is of fundamental interest to understand how the storage, manipulation, and transmission of information utilizing quantum systems are influenced by the fact that these processes take place in a relativistic spacetime. In particular, many studies in RQI have been focused on the effects of non-uniform motion on entanglement, the main resource of quantum information protocols. Early investigations in this direction were performed in highly idealized settings that prompted questions as to the practical accessibility of these results. To overcome these limitations it is necessary to consider quantum systems that are in principle accessible to localized observers. In this thesis we present such a model, the rigid relativistic cavity, and its extensions, focusing on the effects of motion on entanglement and applications such as quantum teleportation. We study cavities in (1+1) dimensions undergoing non-uniform motion, consisting of segments of uniform acceleration and inertial motion of arbitrary duration that allow the involved velocities to become relativistic. The transitions between segments of different accelerations can be sharp or smooth and higher dimensions can be incorporated. The primary focus lies in the Bogoliubov transformations of the quantum fields, real scalar fields or Dirac fields, confined to the cavities. The Bogoliubov transformations change the particle content and the occupation of the energy levels of the cavity. We show how these effects generate entanglement between the modes of the quantum fields inside a single cavity for various initial states. The entanglement between several cavities, on the other hand, is degraded by the non-uniform motion, influencing the fidelity of tasks such as teleportation. An extensive analysis of both situations and a setup for a possible simulation of these effects in a table-top experiment are presented.

In this thesis, I present a semiclassical and quantum mechanical study of a biased superlattice with a tilted magnetic field applied. This system exhibits non-KAM chaotic behaviour which can be controlled by the ratio between the cyclotron and Bloch frequencies. I will use a semiclassical model to show that electron trajectories become unbounded when this ratio takes an integer value. These extended electron trajectories cause peaks in the electron drift-velocity, which lead to current enhancements calculated using a drift-diffusion model. Furthermore, I will explain this current enhancement with reference to the electric field and charge carrier density across the superlattice. These results will then be compared to experimentally measured current-voltage characteristics. A second superlattice is also studied, which has a high probability of interminiband tunnelling. I will outline several theoretical models to account for interminiband tunnelling and will ultimately use an empirical method. The current-voltage results obtained via this method will then be compared to experimental data. Finally, I will use a quantum mechanical model to determine the electron eigenstates for the first superlattice. These quantum mechanical eigenstates will be compared to the semiclassical results to determine the degree of correspondence between the two models. Furthermore, I will use the eigenstates to calculate the energy level structure of the system and investigate how this varies for different applied field strengths. Ultimately, I will suggest a combined band transport plus scattering model to explain experimental current-voltage data obtained for high magnetic fields.

Firstly, the origin of the electron correlation problem is outlined and some approaches to its solution are discussed. In Part I, the difference between the exact and Hartree Fock (HF) inter-electronic potentials experienced between a pair of electrons, known as the fluctuation potential, is used to investigate the effect of correlation on small atoms. They are analysed in terms of radial and angular components of correlation and the dominance of angular-based correlation for a large nuclear charge is seen. In Part II, a new technique for examining the effects of electron correlation on molecular systems is developed. This is subsequently used to investigate the ground states of the H2 and H+3 molecules in position and momentum-space. By employing a natural orbital analysis, it was found for molecules that correlation could be examined in terms of the redistribution in electronic probability parallel to the bond (z-correlation), axially around the bond (o-correlation) and perpendicular to the bond in all directions (p-correlation). The origins of these components were analysed mathematically and their effects on the two-particle electron density were displayed. In position-space, although z-correlation was found to be the most dominant, all types of correlation were seen to increase the mean inter-electronic separation. In momentum-space, however, o and p-correlation acted to increase the mean inter-electronic momentum whereas z-correlation acted in opposition to this and had the effect of increasing the probability of locating both electrons travelling parallel to the bond in the same direction. This was compared with the work performed on atomic systems and the HeH+ molecular ion. For the electron-deficient, the investigation provided evidence to suggest that there are three distinct 'bonding regions' bent towards the centre of the molecule.

No description available.

The work described in this thesis is principally concerned with the analyses at high resolution (∼ 0.05 cm-1) of the infrared gas phase bands of symmetric and asymmetric top molecules. The species studied are isotopic forms of ethane, ethylene and diborane. In the case of diborane the derived rotation, vibration and vibration - rotation constants have been further used to determine an accurate harmonic potential function and the precise molecular structure. Complete analyses have been performed for the nu2, nu 9, nu11 and nu2 fundamentals of CH3CD 3 and 13CH3CD3. Sets of upper state parameters are determined along with an estimate of the ground state centrifugal distortion constant, DK, for each isotopic species. Perturbations in the nu9 band are accounted for in terms of an A1 - E Coriolis interaction with nu3 and in the nu11 band in terms of the combined effects of an A1 - E Coriolis interaction with nu4 and an E(+/- z) ↔ E (= z) interaction with nu10. A small, localised perturbation in is identified as due to higher order rotational resonance with 2nu92. All first and second order Coriolis interaction parameters are determined. High resolution infrared studies of isotopic ethylenes have been undertaken in the region below 2000 cm-1. Accurate vibration and rotation parameters for the fundamentals of C2H4 and C2 D4 are determined. A full upper state rovibration analysis of the nu7 fundamental of C2D4 is achieved, once the various effects of indirect Coriolis interaction with the inactive nu 4 torsion vibration are taken into account. Several localised perturbations are identified and from these the band centre of the inactive nu4 vibration is estimated accurately. Complete analyses of the nu2, nu 12, 2nu7 and 2nu8 bands of H2CCd 2 reported. Localised perturbations are identified and taken into account in the analyses, enabling the perturbing vibrational levels to be located accurately and the interaction parameters to be determined. Ground state rotation and quartic distortion constants are obtained for 11B2H6 and 11B2D6 from the analyses of the nu17 and nu18 type-A and nu14 and nu9 + nu15 type-C bands of 11B2D6 . Sets of upper state parameters are determined for all vibration levels studied and several localised perturbations are observed and identified. The data obtained from these and previous spectroscopic studies of diborane allow a precise determination of the empirical harmonic potential function to be made for the first time. Thirty of the thirty three independent force constants are determined with numerical significance. The physical significance of the values is probably best demonstrated by the close agreement throughout with scaled ab initio force constants from two independent sources. Finally the availability from this and previous work of 12 precisely determined ground state spectroscopic rotation constants for isotopic diboranes, and a physically realistic harmonic potential function, enables the ground state ro substitution rs, zero-point average r z, and equilibrium r structures to be calculated. The rz and re parameters are entirely compatible with, but more accurately determined than, those available from electron diffraction studies.