This thesis describes an experimental study of the electronic properties of the dilute nitride GaAs1¡xNx alloy. This is a semiconductor belonging to a class of highly mismatched III-N-V alloys. The incorporation of isoelectronic N on the pnictide (e.g. As) site of GaAs gives rise to a highly localised electronic state, whose energy level is resonant with the continuum of conduction band (CB) states of the host GaAs lattice. The interaction between these two sets of states causes the formation of a fully developed energy gap in the CB of the host crystal and makes possible the observation of a novel type of negative differential conductance (NDC) effect. The NDC in GaAs1¡xNx is qualitatively different from the NDC occurring in transferred electron devices (Gunn diodes) and semiconductor superlattices (SLs) and has potential for novel terahertz (THz) device applications. The emphasis of the thesis is on the experimental study of the non-linear electron dc dynamics in GaAs1¡xNx that arises when electrons are accelerated in the non-parabolic CB of GaAs1¡xNx. It also includes an investigation of the coupling of electrons to THz radiation by the measurement of harmonic generation of ac current and of changes in the dc conductivity in the presence of an applied THz radiation. The rectification effects revealed in our experiments indicate that the mechanism giving rise to NDC is a fast ( 10¡12 s) process. The fast response in time of the current is in agreement with previous calculations of the ac electron dynamics in GaAs1¡xNx predicting that the maximum response frequency associated with the NDC is governed by the time of ballistic acceleration of electrons to the N-level and that this lies in the THz frequency range. The experimental results are discussed in terms of different theoretical models and mechanisms, including the band anticrossing model, space-charge-limited current instabilities, magnetophonon resonance and classical rectification theory.

In this thesis we investigate the stationary properties and formation process of a class of nontopological solitons, namely Q-balls. We explore both the quantum-mechanical and classical stability of Q-balls that appear in polynomial, gravity-mediated and gauge-mediated potentials. By presenting our detailed analytic and numerical results, we show that absolutely stable non-thermal Q-balls may exist in any kinds of the above potentials. The latter two types of potentials are motivated by Affleck-Dine baryogenesis, which is one of the best candidate theories to solve the present baryon asymmetry. By including quantum corrections in the scalar potentials, a naturally formed condensate in a post-inflationary era can be classically unstable and fragment into Q-balls that can be long-lived or decay into the usual baryons/leptons as well as the lightest supersymmeric particles. This scenario naturally provides the baryon asymmetry and the similarity of the energy density between baryons and dark matter in the Universe. Introducing detailed lattice simulations, we argue that the formation, thermalisation and stability of these Q-balls depend on the properties of models involved with supersymmetry breaking.

In this thesis we describe numerical simulations performed in one- and two-dimensions of a theoretical granular model called the Random Force Model. The properties of non-equilibrium steady state granular media, which this model is a simple example of, are still hotly debated. We begin by observing that the one-dimensional Random Force Model manifest multi-scaling behaviour brought on by the clustering of particles within the system. For high dissipation we find that the distribution of nearest neighbour distances are approximately renormalisable and devise a geometrical method that accounts for some of the structural features seen in these systems. We next study two-dimensional systems. The structure factor, S(k), is known to vary, for small k, as a power-law with an exponent D_f, referred to as the fractal dimension. We show that the value of the D_f is unchanged with respect to both dissipation and particle density and that the power-law is different from that given in any previous study. These structural features influence the long distance behaviour of individual particles by affecting the distances travelled by particles between consecutive collision. The velocity distribution, P(v), is known to strongly deviate away from Maxwell-Boltzmann statistics and we advocate that the velocity distributions have asymptotic shape which is universal over a range of dissipation and particle densities. This invariance in behaviour of the large-scale structure and velocity properties of the two-dimensional Random Force Model leads us to develop a new self-consistent model based around the motion of single high velocity particles. The background mass of low velocity particles are considered to be arrange as a fractal whereby the high velocity particles move independently in ballistic trajectories between collisions. We use this description to construct the high velocity tail of P(v), which we find to be approximately exponential. Finally we propose a method of structure formation for these systems that builds self-similarity into the system by consecutively fracturing the system into smaller parts.

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.