Carbon nanocones are the fifth equilibrium structure of carbon, first synthesized in 1997. They have been selected for investigating hydrogen storage capacity, because initial temperature programmed desorption experiments found a significant amount of hydrogen was evolved at ambient temperatures. The aim of this thesis was to study the effect of impregnation conditions on metal catalyst dispersion and to investigate whether the metal loaded cones had improved hydrogen storage characteristics. Pre-treatment of carbon nanocones with hydrogen peroxide was carried out, followed by metal decoration in aqueous solution by an incipient wetness technique. Two methods of reducing the metal catalyst have been applied: in hydrogen at room temperature (RT) and in an aqueous solution of NaBH4. X ray diffraction (XRD) technique confirmed the complete metal reduction and transmission electron microscope (TEM) analysis showed that the reduction technique affected the catalyst dispersion. Very fine dispersions of ca. 1 nm diameter metal clusters at catalyst loadings of 5 wt% were achieved and high dispersions were retained for loadings as high as 15 wt%. Hydrogen uptakes at RT were measured and an increase with metal loading was observed. In comparison the same route of pre-treatment and metal impregnation has been done over graphite nanofibres (GNF) and the hydrogen uptake showed an adsorption superior of the cumulative contribution of the substrate and metal catalyst attributing this to hydrogen spillover. The GNF have been impregnated also with another metal catalyst Ni showing as well the phenomenon of hydrogen spillover. The attempt to impregnate the carbon nanocones with a mixture of Pd-Ni, Pd-Cu and Pd-Ag resulted in an increase of hydrogen uptake for the first two but a decrease for the last of these. The carbon nanocones have been also impregnated with a Mg organometallic precursor dibutyl magnesium (DBM) and then decomposed without the use of hydrogen environment synthesizing successfully MgH2. The stoichiometry and the enthalpy of this decomposition have been studied. Furthermore, the DBM has been mixed with another hydride LiALH4 and the decomposition reaction of the complex hydride has been studied.

Einstein’s General Relativity has been our best theory of gravity for nearly a century, yet we know it cannot be the final word. In this thesis, we consider modifications to General Relativity, motivated by both high and low energy physics. In the quantum realm, we focus on Horava gravity, a theory which breaks Lorentz invariance in order to obtain good ultraviolet physics by adding higher spatial derivatives to the action (improving propagator behaviour in loops) but not temporal (avoiding Ostrogradski ghosts). By using the Stückelberg trick, we demonstrate the necessity of introducing a Lorentz violating scale into the theory, far below the Planck scale, to evade strong coupling concerns. Using this formalism we then show explicitly that Horava gravity breaks the Weak Equivalence Principle, for which there are very strict experimental bounds. Moving on to considering matter in such theories, we construct DiffF(M) invariant actions for both scalar and gauge fields at a classical level, before demonstrating that they are only consistent with the Equivalence Principle in the case that they reduce to their covariant form. This motivates us to consider the size of Lorentz violating effects induced by loop corrections of Horava gravity coupled to a Lorentz invariant matter sector. Our analysis reveals potential light cone fine tuning problems, in addition to evidence that troublesome higher order time derivatives may be generated. At low energies, we demonstrate a class of theories which modify gravity to solve the cosmological constant problem. The mechanism involves a composite metric with the square root of its determinant a total derivative or topological invariant, thus ensuring pieces of the action proportional to the volume element do not contribute to the dynamics. After demonstrating general properties of the proposal, we work through a specific example, demonstrating freedom from Ostrogradski ghosts at quadratic order (in the action) on maximally symmetric backgrounds. We go on to demonstrate sufficient conditions for a theory in this class to share a solution space equal to that of Einstein’s equations plus a cosmological constant, before determining the cosmology these extra solutions may have when present.

Experiments have been performed at high B/T to try to establish the existence and value of an anisotropy temperature (Ta) for pure 3He, and for 6.2% and 0.7% 3He-4He mixtures. The anisotropy of diffusion in dilute Fermi gases as the temperature T goes to zero has been predicted, though experimental evidence for such anisotropy has not been universally accepted. Finite size effects have required careful analysis of the theory of the cell for the 6.2% mixture. This alters the result as determined by the usual Leggett-Rice formula. Further investigation, beyond the scope of this thesis, is currently underway for the case of pure 3He. The possibility of using a quartz tuning fork as a viscometer has also been investigated. It is shown that tuning forks can be used field-inpendently above 3 mK in saturated 3He-4He mixtures, and to detect the superfluid A and B-phase transitions in pure 3He. It is strongly suggested from the data that the tuning fork has great potential as a high-field viscometer; however further experiments are required to fully appreciate its useful range, in both normal and superfluids.

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.