This thesis is devoted to the study of the non-radiative process of Interatomic (Intermolecular) Coulombic Decay (ICD) in clusters. The aims of this thesis are two-fold: firstly we study ICD in the inner-valence-ionised endohedral fullerene complexes, such as (2s^1)Ne^+@C_60, where it is ultrafast due to the many available decay channels. We investigate the open question of the dependence of the ICD rate on the location of the endohedrally confined ion. Qualitative analysis shows that once the symmetry of the endohedral system is lowered by the departure of a rare gas atom from its equilibrium position in the centre of the cage, multipole plasmon resonances can be excited by energy transfer from the inner-valence-ionised ion to the cage. Nevertheless, our quantitative analytical and ab initio numerical studies lead to the conclusion that the total ICD width is remarkably stable across broad range of geometries. It turns out that the multipole plasmon excitation is negligible and the well-known dipole fullerene plasmon is the one defining the ICD time scale. Secondly we focus our attention onto inner-valence vacancies that are not energetic enough to decay via ICD. We propose that under such conditions, an ICD-like electronic process may still be induced by an incident photon. We call the new process single photon laser-enabled ICD (spLEICD). We for the first time investigate spLEICD in a series of van der Waals and hydrogen-bonded clusters. Our results demonstrate that the spLEICD cross-sections in hydrogen-bonded systems are larger than in van der Waals ones, whereas polyatomic van der Waals clusters lead to a more efficient spLEICD process than the van der Waals diatoms. We analyse the dependence of the spLEICD cross-section on the inter-atomic distance in a cluster showing analytically that it obeys the 1/R^6 law at large distances. This analysis is confirmed by our \textit{ab initio} numerical calculations. This strong distance-dependence may allow spLEICD to be used as a novel spectroscopic technique for the study of processes which occur in different spatial regions of molecules or clusters.

In this thesis we apply the methods of partition functions to massive superstring spectra and the moduli spaces, or spaces of zero-energy configurations, of supersymmetric QCD gauge theories. In the first part of this thesis we consider the massive covariant perturbative superstring spectra of compactifications of the type I open superstring preserving 4, 8 or 16 supercharges. There are an enormous number of ways in which the required amount of symmetry can be obtained, but here we concentrate on the `universal' states that are present in every possible compactification preserving that amount of supersymmetry. For each super-Poincar\'e representation we derive the multiplicity generating function, or the power series counting the number of times that representation occurs at each mass level, and from these we derive empirically the stable pattern or leading Regge trajectory that these multiplicity generating functions approach in the limit of large spin. For the mathematically tractable and phenomenologically relevant case of 4 supercharges we also derive these power series analytically and see that they agree with the empirical ones. In the second part we introduce the type of partition functions called Hilbert series, which count the number of algebraically or linearly independent polynomials at each graded level of a graded algebraic structure such as a (graded) ring, module or ideal. In supersymmetric gauge theories the algebraic structure is the chiral ring which is generated by the gauge-invariant operators of the theory. The specific theories we consider are supersymmetric generalizations of QCD, or SQCD, with exceptional or related (by sequence or folding of the Dynkin diagram or Higgsing) gauge groups with specified numbers of flavours of matter in specific representations. We show, as for theories with classical gauge groups, that the moduli spaces are Calabi-Yau manifolds and also demonstrate relations between the Hilbert series of SQCD theories related by Higgsing on one or more flavours of matter in specific representations.

Recent developments in laser science have made it possible to experimentally study ultrafast electron dynamics in atoms and molecules directly by using ultrashort pulses on the order of tens of attoseconds. It is paramount, both for current understanding and planning of future experiments and applications, that we decipher how short pulses interact with the medium. We model attosecond dynamics of multi-electron systems following three themes: (1) propagation and distortion of pulses in absorbing noble gases, (2) simulation of atoms and molecules under the effects of pump and probe pulses, (3) coherence and polarization effects on transient absorption. First, using the Kramers-Kronig relations and a fast and stable numerical algorithm based on Mobius transformations, we model the distortion of XUV pulses propagating in noble gases. Our simulations show rich features including pulse stretching, partial narrowing, partial apparent super-luminality, and tail development. Second, we deploy the density matrix formalism using Lindblad terms and the three Hilbert spaces method, incorporating multi-channel and Auger ionization compactly and consistently, to model coherence observed in pump-probe attosecond transient absorption studies of Kr II. We explain how coherent noble cation states are produced. Density matrix elements for the excited Kr II 3d_3/2 and 3d_5/2 levels caused by a resonant z-polarized 80 eV 150 as probe pulse are simulated and the resulting population densities and induced dipole moments are analyzed, including nonlinear contributions. In order to model pulse propagation, we develop absorption theory for arbitrary polarization angle and point out how coherence effects distort the Beer-Lambert law and discuss experimental implications. Third, we investigate non-adiabatic effects in attosecond dynamics in molecules driven by a laser field. We use the Algebraic Diagrammatic Construction method and Arnoldi-Lanczos TDSE programs to simulate N2 and oligocenes for 400 nm, 800 nm and 1.6 micron wavelengths with various laser intensities and polarizations. We determine the onset of non-adiabaticity in N2, benzene and naphthalene. Last, but not least, I describe my experimental contribution to the new Imperial College beamline.

Artificial Spin Ice (ASI), comprised of ferromagnetic nanobars in a honeycomb geometry, attracts much attention since it is a directly imageable frustrated system which exhibits rich physics including ice-rule behaviour and magnetic monopole excitations. ASI's nanobars undergo domain wall mediated magnetic reversal in external fields. Understanding and indeed controlling the trajectories of field driven domain walls and hence the order in which ASI's nanobars are reversed is a crucial step towards mapping out ASI's full functionality for potential applications. In this thesis, trajectories of domain walls during the early stages of ASI's magnetic reversal are studied. Data showing domain walls executing non-random walks in the transverse domain wall regime and random walks in the vortex domain wall regime is presented. The former behaviour is linked to the domain wall's chirality, and as such, attempts to control a domain wall's initial chirality via triangular injection pads are discussed. In addition, ways in which a vortex domain wall's chirality may be controlled with ellipsoidal hole obstructions are shown. Artificial Dipolar 2D-XY, a complementary system to ASI, also promises interesting behaviour. In this new frustrated architecture, individual nanobars are replaced with single domain nanodiscs whose magnetisations can point in any in-plane direction. In this thesis, intriguing results from preliminary experiments on this new system are presented. One of the best techniques used to study the magnetisations of nanostructures such as those described above is Lorentz Transmission Electron Microscopy (LTEM). Since the contrast yielded for unusual magnetic states was not well documented, software called Micromagnetic Analysis to Lorentz TEM Simulation (MALTS) was developed in order to aid in analysis of LTEM images. MALTS can simulate the LTEM contrast of any magnetic object of any size, shape or state. A description of its full functionality is also included in this thesis.

Experimental results utilising novel diagnostic techniques focussing on spatial resolution of shock-induced sliding phenomena at multi-material aluminium - stainless steel dry metallic contact interfaces are presented. Relative particle velocities of 50 m s⁻¹ are generated at the sliding interface via an intrinsic impedance mismatch between the material components, driven by gas gun flyer plate impact. Results are first presented for the metallography of recovered target samples from shock-induced sliding contact interfaces where the intrinsic grain structure is utilised as a fiducial marker to provide a measure of the sub-surface deformation experienced. Two distinct mutually exclusive scales of deformation were identified extending over millimetre and micrometre depths with relatively low and high free surface sliding velocities measured for these respectively using optical velocimetry. Further experimental results are presented for spatially resolved velocimetry of shock-induced sliding at planar material interfaces utilising a line-VISAR diagnostic. Experiments are conducted over 3 mm and 15 mm interface length scales with the contact interface orientated at 0.0° and 5.0° relative to the direction of loading. Specific material pairings of aluminium 1050 and aluminium 7068 paired independently with stainless steel 316 were utilised. An initial large scale experiment was found to be suggestive of the role of gaps at the contact interface, estimated to be 35 μm in size via comparison of the velocimetry data with hydrocode models. Further mesoscale experiments are suggestive of the role of re-shock and release waves generated at the contact face co-incident with the breakout of the elastic and plastic shock fronts, defining the velocimetry profile in close vicinity of the contact face over the timescales measured.

In this thesis I discuss work that has been carried out on the dynamics of a Bose Einstein condensate of Rb 87 produced near an atom chip. A Bose Einstein Condensate (BEC) is a quantum state of matter where a single quantum state becomes occupied by a macroscopic number of identical Bosons. In our case this is achieved by cooling a system of trapped identical rubidium 87 atoms to its ground state. To reach temperatures of condensation we initially laser cool atoms from room temperature, before loading them into a magnetic trap. The magnetic trap is produced through a combination of uniform magnetic fields from coils outside our vacuum chamber and currents running through wires on an atom chip. The atom chip is a microfabricated device, produced by a coating a silicon chip with a thin layer of gold and etching wires into it. Together, these fields create a magnetic field minimum 120μm from the surface of the chip which can be used to confine low field seeking hyperfine states of the atom in an elongated harmonic trap. Once the atoms are confined in the magnetic trap we used force evaporative cooling out to reach the phase space densities required for Bose Einstein condensation. The BEC is used to investigate the relative dynamics between the fraction of the atoms in the condensate to those not in the condensate. Our atom chip provided a suitable environment to investigate this due to fragmentation of the magnetic potential close to the chip. Small imperfections in the wires on our atom chip mean that the trapping potential isn't smooth. Small regions of higher trapping frequency - or fragments - are formed. Due to the small size of these fragments it is possible to find a position where a condensate can form in the fragment, and see a potential of high frequency, whereas a non-condensed atom will see a lower frequency potential. We exploit this to set the condensed fraction moving relative to the non condensed part and investigate the subsequent damping of their motion relative to each other.

For 35 years, laser-cooled trapped ions have been at the frontier of progress in quantum computing, quantum simulation and precision measurement, and remain one of the most valuable tools in these fields to this day. Most of these experiments are predicated upon or benefit from the ability to place ions in the motional quantum ground state, a technique that was first demonstrated in radio-frequency ion traps 25 years ago. For a range of crucial experiments that are impossible to conduct in radiofrequency traps or are not well suited to this architecture, Penning traps provide an important alternative. However, the performance of Penning traps had been limited by the fact that ground-state cooling was yet to be achieved in such a system. This thesis reports the first demonstration of resolved-sideband cooling in a Penning trap, for 40Ca+ions cooled with light at 729-nm, achieving a ground state occupation of 99% in one dimension. Demonstrations of the coherent manipulations possible at this level of confinement are presented. The ion heating rate is measured and although higher than might be expected given the unusually large ion-electrode distance remains amongst the lowest reported in any trap to date. Achieving this result required the development of a number of new experimental systems and major upgrades to the stability and reliability of the experiment, the details of which are also given. The thesis also presents theoretical work into the use of two-dimensional Coulomb crystals in a Penning trap as a resource for quantum information. Using the symmetries of the crystal, we find that it is possible to engineer complex entangled states, specifically two small quantum error correcting codes, using a very small number of global entangling pulses. Efficient entanglement protocols such as these are vital for the implementation of useful quantum error correction.

Quantum chemistry based simulations allow us to explore the length and time scales which are experimentally inaccessible. In particular, these simulations bring a unique perspective on processes governed at the nanoscale by electronic interactions such as charge transfer. In this thesis, I present a framework for the multiscale simulation of hole transfer between dye molecules tethered on (101) TiO2 surfaces as in Dye Sensitized Solar Cells (DSSC). At the molecular level, I use methods derived from ground state density functional theory to calculate the reorganization energy (λ_tot) including ionic solvent effects, and electronic coupling (J_ij) distributions representing the conformational disorder of a dye monolayer. At the nanoscale, I use the semi-classical non adiabatic Marcus's equation to calculate the rate of hole transfer in the high temperature limit from λ_tot and J_ij. At the macroscopic scale, I calculate hole diffusion coefficients from kinetic Monte Carlo (KMC) simulations and validate my results by comparing with experimental data, when available. I find that the polar electrolytes used in DSSC contribute to 80% of the total reorganization energy of hole exchange. By including the effect of structural rearrangement of the dyes on various timescales, I show that large amplitude fluctuations of the tethered dyes at the microsecond timescale may enable charges to escape configurational traps. However, the analysis of Quasi Elastic Neutron Scattering (QENS) data on dye sensitised TiO2 nanoparticles suggests that the dyes are immobile between tens of picoseconds and few nanoseconds. This implies that the hypothesised dynamical rearrangement of the dye monolayer at the microsecond timescale originates from the collective motion of the molecule and its neighbours. These findings suggest that charge transport across disordered dye monolayers is enabled by the structural rearrangement of the molecules while the low measured diffusion coefficients (~10^-8 cm^2.s^-1) arise from the high polarity of the medium.

In recent years, time-dependent density-functional theory (TDDFT) has been the method of choice for calculating optical excitations in medium sized to large systems, due to its good balance between computational cost and achievable accuracy. In this thesis, TDDFT is reformulated to fit the framework of the linear-scaling density-functional theory (DFT) code ONETEP. The implementation relies on representing the optical response of the system using two sets of localised, atom centered, in situ optimised orbitals in order to ideally describe both the electron and the hole wavefunctions of the excitation. This dual representation approach requires only a minimal number of localised functions, leading to a very efficient algorithm. It is demonstrated that the method has the capability of computing low energy excitations of systems containing thousands of atoms in a computational effort that scales linearly with system size. The localised representation of the response to a perturbation allows for the selective convergence of excitations localised in certain regions of a larger system. The excitations of the whole system can then be obtained by treating the coupling between different subsystems perturbatively. It is shown that in the limit of weakly coupled excitons, the results obtained with the coupled subsystem approach agree with a full treatment of the entire system, with a large reduction in computational cost. The strengths of the methodology developed in this work are demonstrated on a number of realistic test systems, such as doped p-terphenyl molecular crystals and the exciton coupling in the Fenna-Matthews-Olson complex of bacteriochlorophyll. It is shown that the coupled subsystem TDDFT approach allows for the treatment of system sizes inaccessible by previous methods.

Future upgrades of the CERN Large Hadron Collider (LHC) may demand improved cleaning performance of its collimation system. Very efficient collimation is required during regular operations at high intensities, because even a small amount of energy deposited on superconducting magnets can cause an abrupt loss of superconducting conditions (quench). The present collimation system has accomplished its tasks during the LHC Run I very well, where no quench with circulating beam took place with up to 150 MJ of stored energy at 4 TeV. On the other hand, uncertainty remains on the performance at the design energy of 7 TeV and with 360 MJ of stored energy. In particular, a further increase up to about 700 MJ is expected for the high luminosity upgrade (HL-LHC), where improved cleaning performance may be needed together with a reduction of collimator impedance. The possibility to use a crystal-based collimation system represents an option for improving both cleaning performance and impedance compared to the present system. A bent crystal can in theory replace primary collimators and steer all halo particles onto one single absorber, providing better cleaning with reduced impedance than the present multi-stage collimation system, which is based on massive amorphous blocks of material that surround the beam. Although promising results on the principle of crystal collimation were obtained during experimental tests at the CERN Super Proton Synchrotron (SPS), feasibility studies at the LHC are mandatory before relying on this approach for future upgrades. The main goal of this Ph.D. thesis is the design of an optimised prototype crystal collimation system for these tests in the LHC, which has been installed during April 2014.