The subject of this thesis is the study of a particular open quantum system consisting of a resonator coupled to a superconducting single electron transistor (SSET). The theoretical model we use is applicable to both mechanical and superconducting stripline resonators leading to a large parameter regime that can be explored. The SSET is tuned to the Josephson quasi-particle resonance, in which the transport occurs via Cooper pairs coherently tunnelling across one junction followed by the incoherent tunnelling of quasi-particles across the other. The SSET can be thought of as an artificial atom since it has a similar energy level structure and transitions to an atom. We investigate to what extent the current and current noise through the SSET can be used to infer the state of the resonator. In order to carry out these investigations we describe the system with a Born-Markov master equation, which we solve numerically. The evolution of the density matrix of the system is described by a Liouvillian superoperator. In order to better understand the results we perform an eigenfunction expansion of the Liouvillian, which is useful in connecting the behaviour of the resonator to the current noise. The mixture of coherent and incoherent processes in the SSET leads to interesting back action effects on the resonator. For weak coupling the SSET acts as an effective thermal bath on the resonator. Depending on the operating point the resonator can be either heated or cooled in comparison to its surroundings. In this regime we can use a set of mean field equations to describe the system and also capture certain aspects of the behaviour with some simple models. For sufficient coupling the SSET can drive the resonator into states of self-sustained oscillations. At the transition between stable and oscillating states of the resonator we also find regions of co-existence between oscillating and fixed point states of the resonator. The current noise provides a way to identify these transitions and the state of the resonator. The system also shows analogies with quantum optical systems such as the micromaser. We calculate the linewidth of the resonator and find deviations from the expected behaviour.

In this work we investigate the dynamics of Bose-Einstein condensates (BECs) in inhomogeneous potential landscapes. As this research field continues to develop, more attention will focus on non-equilibrium systems, on potential applications that use condensates, and on the integration of cold atoms with other physical systems. This thesis covers all of these areas. We begin by recapping the historical background of condensate physics, with a definition of the condensed phase and discussion of various analytical quantities of relevance to this work. The Landau picture of supefluidity and predictions of its breakdown, given by the Landau criterion, is particularly pertinent to the results on supersonic flow in an inhomogeneous system. After outlining current experimental procedures, we present a computationally efficient modelling technique, used in our numerical simulations of atomic condensates. We then use this technique to study the dynamics of supersonic condensate flow, in the presence of a perturbing potential. Normally one would expect this situation to introduce disturbances, known as Landau excitations into the system, potentially destroying it. However, we find, under certain circumstances, complete suppression of Landau excitations: a behaviour that has not, to our knowledge, been previously observed. The efficiency of our chosen modeling technique allowed the possibility to conduct the large phase space campaigns necessary to find these special circumstances. On investigation, the mechanism resulting in the suppression of these Landau excitations is continuously related to the presence of transmission resonances in an equivalent linear quantum system. This demonstration of a link between linear and non-linear quantum regimes is of great interest in understanding possible behaviour in other non-equilibrium superfluid systems. Finally, we consider the magnetic fields from small scale (~ 1 µm) quantum electronic devices fabricated within a two-dimensional electron gas (2DEG). We demonstrate that atomic condensates provide a powerful tool for imaging these fields, or indeed similar fields created by other structures. Using a Fourier method, we show that the field profile that would be measured by the condensate can be used to recreate the current density of the 2DEG structure. The spatial resolution of this current mapping technique is limited only by the separation of the condensate from the current-carrying structure. We also show that quantum electronic conductors in 2DEGs are well suited to form a new generation of atom chips capable of trapping atoms < 1 µm away, thereby reducing both the size and power requirements of chip-trap potentials.

This thesis investigates the equilibrium and dynamic properties of stochastic systems of varying complexity. The dynamic properties of lattice models -- the 1-d Ising model and a 3-d protein model -- and equilibrium properties of continuous models -- particles in various potentials -- are presented. Dynamics are studied according to a large deviation formalism, by looking at non-equilibrium ensembles of trajectories, classified according to a dynamical order parameter. The phase structure of the ensembles of trajectories is deduced from the properties of large-deviation functions, representing dynamical free-energies. The 1-d Ising model is studied with Glauber dynamics uncovering the dynamical second-order transition at critical values of the counting field 's', confirming the analytical predictions by Jack and Solich. Next, the dynamics in an external magnetic field are studied, allowing the construction of a dynamic phase diagram in the space of temperature, s-field and magnetic field. The dynamic phase diagram is reminiscent of that of the 2-d Ising model. In contrast, Kawasaki dynamics give rise to a dynamical phase structure similar to the one observed in kinetically constrained models. The dynamics of a lattice protein model, represented by a self avoiding walk with three different Hamiltonians, are studied. For the uniform Go Hamiltonian all dynamics occurs between non-native and native trajectories, whereas for heterogeneous Hamiltonians and Full interaction Hamiltonians a first-order dynamical transition to sets of trapping trajectories is observed in the s-ensemble. The model is studied exhaustively for a particular sequence, constructing a qualitative phase diagram, from which a more general dynamic behaviour is extrapolated. Lastly, an estimator for equilibrium expectations, represented by a transition matrix in an extended space between temperatures and a set of discrete states obtained through the discretisation of a continuous space, is proposed. It is then demonstrated that this estimator outperforms conventional multi-temperature ensemble estimates by up to three orders of magnitude, by considering three models of increasing complexity: diffusive particles in a double-well potential, a multidimensional folding potential and a molecular dynamics simulations of alanine dipeptide.

This dissertation studies the dynamics of atomic Bose-Einstein condensates (nEes) and Bose gases in a suddenly modified potential. Firstly, we investigate the correlation between vortex formation and interference in merging Bose-Einstein condensates. This inherent correlation can explain some experiments in which vortices are formed in interfering condensates. Furthermore, we show the interference properties of merging condensates, particularly the relation of interference among colliding, expanding, and merging condensates, which can explain some complex interference phenomena in recent experiments. Secondly, using the truncated Wigner approximation, we investigate the role of quantum fluctuations in different forms on the transport properties of bosonic atoms in a ID optical lattice. The dynamics of transport with respect to quantum fluctuations in the plane-wave modes is distinct from that in the single-harmonic-oscillator modes. The discrepancies are demonstrated in detail. Quantum fluctuations in Bogoliubov modes lead to stronger damping behaviour of the centre-of-mass motion than quantum fluctuations in the plane-wave and single-harmonic-oscillator modes, which is in agreement with the experiment. Thirdly, the role of the relative phase variation and velocity of two low-density condensates, and quantum noise on interference properties are discussed. In particular, the incoherent atoms have significant effect on the interference visibility and microscopic dynamics. Although the interference pattern is not broken by quantum fluctuations, indicating the robust character of this interference, the process of inner correlations and dynamics is very complex and cannot he understood purely with mean-field theory. Finally, we investigate the elementary excitation spectrum and mode functions of a trapped Bose gas by numerically solving the Bogoliubov-De Gennes equation. The characteristic form of the Bogoliubov matrix, determined by the interatomic interactions, and the interaction between atoms and confining potential, specifies excitation spectra and mode functions. The role of these interactions on the properties of spectra and mode functions are shown.

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.