Colloidal nanoparticles exhibit unusual individual and collective behaviour, often associated with interesting electrical, optical or electromagnetic properties. Thiol-passivated colloidal gold nanoparticles possess in addition a self-organising property, which, when the particles are deposited on a substrate, yields a plethora of fascinating patterns. The conditions of formation of these patterns are investigated, in order to understand the principles of - and gain control over - non-equilibrium self-organisation following drop evaporation. The work presented in this thesis relies mostly on experimental observations, although the results are supported by numerical simulations carried out in the group and based on modified versions of the model developed by Rabani et al. in 2003 [1]. A novel deposition method is introduced, which provides controllable conditions for the occurrence of a wide variety of patterns, including close-packed monolayers of nanoparticles. Pattern and surface characterisation is achieved by combined microscopy techniques - atomic force microscopy (AFM) and real-time contrast-enhanced optical microscopy. The influence on pattern formation of the nanoparticle-solvent-substrate interactions is studied by altering the physical properties of all three components (substrate, solvent and nanoparticles). The experimental set-up allows a meniscus-driven evaporation of the solvent of the nanoparticle solution and enables monitoring of drying front instabilities during the dewetting process. The effects of these instabilities on pattern formation are investigated and highlight a strong contribution of free excess ligands. We have focused on two specific types of patterns which emerge in these experiments : fingering structures and nanoparticle rings. The former are reminiscent of patterns that form in a number of other systems, a process usually called "viscous fingering". A thorough investigation reveals that the mechanism of formation of such patterns involves the combination of specific experimental conditions and at least two different dewetting processes, with different time and length scales. A "pseudo-3D" Monte Carlo model recreates such conditions and yields simulated results which are in good qualitative and quantitative agreement with experimental results. On the other hand, nanoparticle rings, although they are a recurrent type of pattern observed in nanoparticle assemblies [2, 3], form according to a mechanism which is not yet fully understood. We show however that wetting properties play a central role in ring formation and growth. As in the case of fingering structures, a narrow range of parameters has been determined, via an exhaustive experimental investigation, which favours the occurrence of nanoparticle rings. For all the nanoparticle assemblies studied in this thesis (close-packed monolayers, fingering structures and nanoparticle rings), the deduction of pattern formation mechanisms from experimental observation (and simulations) relies on the very high degree of reproducibility that it is possible to attain using the combination of a meniscus-driven evaporation, a very fine tuning of experimental conditions and nanoparticle-solvent-substrate interactions, and a systematic cross-characterisation by complementary imaging techniques.

We investigate the dynamics of the geometric transitions associated to compactified spacetimes. By including the effects of gravity we are able to follow the evolution of collapsing cycles as they attempt to undergo a topology changing transition. We perform investigations where we add a perturbation to the momentum of a static solution and observe the consequences this has on the spacetime, looking for evidence of black hole formation or collapsing cycles which could lead to singular geometry. First we look into two possible four dimensional spacelike solutions to the Einstein equations called instantons. These both have a two-sphere at the origin, these are called bolt singularities. We introduce an initial perturbation to reduce the two-sphere to a point. Rather than achieving this singular geometry we find that either a horizon forms, shielding a curvature singularity, or the cycle re-expands after an initial contraction phase. For the case where a horizon forms we identify the final state with a known analytic black-hole solution. In seven dimensions we simulate the gravitational dynamics of the conifold geometries (resolved and deformed) involved in the description of certain compact spacetimes. As the cycles of the conifold collapse towards a singular geometry we inevitably find that a horizon develops, shielding the external spacetime. The structure of the black hole is examined and we find a candidate for the final state of the collapse. In ten dimensions we investigate the time evolution due to gravitational dynamics of a spacetime which is commonly used in brane-cosmology and string compactifications called the Klebanov-Strassler geometry. Here black holes are sometimes formed but more commonly the cycles are seen to re-expand after reaching a minimum value, showing the stability of the solution against perturbations which would change its size.

In this thesis, experimental evidence of sustained phonon oscillations, from an electrically pumped vertical-cavity SASER device, working in the THz frequency domain is presented. Experimental investigation of injection seeding of phonons at a particular frequency, by optical excitation, is also presented. The experimental evidence of phonon oscillation through SASER action consists of a non-linear increase in the initial rising edge of the ballistically propagating LA phonons signal and an increased directionality of emission, once threshold gain is exceeded. The build-up of phonon oscillation fitted well with the theoretical model, also discussed in this thesis, enabling other attributes of the SASER device such as the gain coefficient, maximum acoustic power and device efficiency to be obtained. The cavity was investigated by means of pump-probe reflectivity measurements. Good quantitative agreement is obtained for the cavity mode frequencies, compared to the calculated reflectance of the cavity modes. Good quantitative agreement of the phonon scattering losses, within the cavity, was also obtained, when compared with theoretical predictions. Also provided is experimental evidence of injection seeding in the SASER devices under different conditions. The SASER device yields analogous characteristics to a seeded laser in that it acts as a phonon amplifier, due to SASER action, for the injected modes. The results contribute not only towards understanding the fundamental principles of achieving SASER oscillations but also towards the possibility of achieving a practical SASER device in the future.

The charge transfer dynamics between adsorbate molecules and surfaces are important for a variety of different technologies but especially for dye-sensitized solar cells. The main aim of this thesis was to study charge transfer between organic molecules and surfaces, especially relating to the situation observed in dye sensitized solar cells. This broad aim can be split into two distinct research objectives. One of these was to study the charge transfer between a Au (111) surface and a variety of different molecules using synchrotron-based photoemission spectroscopy. Resonant photoemission spectra of a C60 monolayer on Au (111) showed distinctive superspectator features which were not observed for the multilayer or clean gold spectra. These features were determined to be resultant from spectator decay involving electrons transferred from the gold substrate to the adsorbed molecule, either in the ground state or during the timescale of the core-hole lifetime. These features were also found for monolayers of bi-isonicotinic, isonicotinic, nicotinic and picolinic acid on gold, but not for the dye molecule, N3, on gold. This suggests that, although charge transfer occurs between the surface and the ligand molecules that constitute N3, no charge transfer occurs between the N3 dye molecule and the gold. The other objective was to determine whether the core-hole clock technique, previously only used in photoemission spectroscopy, could be adapted for resonant inelastic x-ray scattering. For this, bi-isonicotinic acid on TiO2 was studied because this system had already been explored using photoemission spectroscopy. The charge transfer times were measured using the relative decrease in the elastic peaks for the LUMO and LUMO+1 photon energies of the multilayer and monolayer. This gave a similar result to the photoemission studies providing more confidence for using this adaptation in situations where photoemission would be impossible, such as buried interfaces.

In the solid state the rotation of a methyl group is hindered by a potential barrier and at low temperature the rotational motion is characterised by quantum tunnelling. The Pauli Exclusion Principle imposes constraints on the allowable eigenstates of the methyl rotor and leads to a combination of spatial and spin variables. The characteristics of these quantum tunnelling states, labelled A and E, are explored experimentally and methods are investigated for creating prescribed non-equilibrium states. We will investigate and explore the tunnelling polarization associated with the A and E tunnelling-magnetic levels by means of field-cycling NMR. Secondary rf irradiation is used to drive A-E and E-A transitions associated with NMR tunnelling sidebands. This polarization is then transferred to the 1H Zeeman system at a field-dependent level-crossing where the methyl tunnelling frequency equals one or two times the 1H Larmor frequency. The level-crossing contact is a necessary step since the tunnel temperature cannot be measured directly with a pulse. A new pulse sequence is described and the resulting spectra are analogous to the solid effect and dynamic nuclear polarization. Therefore we assign the phrase ‘dynamic tunnelling polarization’ to describe the experiments. Two samples are studied in depth, methyl ethyl ketone and acetophenone which have tunnel frequencies of 495 and 1435 kHz respectively. The experiments investigate the phenomena as a function of a variety of physical parameters in order to determine the fundamental physics.

Surface Plasmons provide a relatively high axial sensitivity and thus are generally used in a thin surface film sensing and imaging. Objective lens based surface plasmon microscopy enables measurement of local refractive index on a far finer scale than the conventional prism based systems. However, researchers find that a trade-off between the lateral resolution and the axial sensitivity exists in the conventional intensity based surface plasmon microscopy. In order to optimize the trade-off, interferometric surface plasmon microscopy was exploited. An interferometric or confocal system gives the so-called V(z) curve, the output response as a function of defocus, when the sample is scanned axially, which gives a measure of the surface plasmon propagation velocity. Considering the complexity of the two arm interferometric system, in this thesis, I show how a confocal system provides a more flexible and more stable alternative. This confocal system, however, places greater demands on the dynamic range of the system. Firstly, the sharp edge of the pupil on the back focal plane of the objective can generate similar effect with the surface plasmon (SPs) ripples; Secondly, the SPs ripples that convey much of the information are much smaller compared to the in focus response which means the confocal system suffers from low signal to noise ratio (SNR). In order to overcome the limitations, I proposed pupil function engineering which was to use a spatial light modulator to modulate the illumination beam profile by using the designed pupil functions with smooth edges. The results show that the sharp edge effect of confocal setup can be greatly reduced and the SNR is improved. Based on this system, I demonstrated that images obtained from the setup are comparable with the two arm interferometric SPR microscope and other wide-field non-SPR microscope. Secondly, I demonstrate the technique of V(α). A phase Spatial Light Modulator (SLM) was applied to replace the previous amplitude SLM. I show how a phase spatial light modulator (i) performs the necessary pupil function apodization (ii) imposes an angular varying phase shift that effectively changes sample defocus without any mechanical movement and (iii) changes the relative phase of the surface plasmons and reference beam to provide signal enhancement not possible with previous configurations using ASLM. Later, I extend the interferometer concept in the confocal system to produce an ‘embedded’ phase shifting interferometer in chapter 6, where I can control the phase between the reference and surface plasmon beams with a spatial light modulator. I demonstrate that this approach facilitates extraction of the amplitude and phase of the surface plasmons to measure of the phase velocity and the attenuation of the surface plasmons with greatly improved signal to noise compared to previous measurement approaches[1]. I also show that reliable results are obtained over smaller axial scan ranges giving potentially superior lateral resolution. In the end of the thesis, future work will be discussed. Firstly, I will propose another technique called ‘artificial’ plasmon. Secondly, I will recommend constructing another system and develop the ideas discussed so the system can work in aqueous environment.

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.