Search

In this thesis I discuss the nature of ‘measurement’ in quantum theory. ‘Measurement’ is associated with several different processes: the gradual imprinting of information about one system onto another, which is well understood; the collapse of the wavefunction, which is ill-defined and troublesome; and finally, the means by which inferences about unknown experimental parameters are made. I present a theoretical extension to an experimental proposal from Leggett and Garg, who suggested that the quantum-or-classical reality of a macroscopic system may be probed with successive measurements arrayed in time. The extension allows for a finite level of imperfection in the protocol, and makes use of Leggett’s ‘null result’ measurement scheme. I present the results of an experiment conducted in Oxford that, up to certain loopholes, defies a non-quantum interpretation of the dynamics of phosphorous nuclei embedded in silicon. I also present the theory of statistical parameter estimation, and discover that a recent trend to employ time symmetric ‘postselected’ measurements offers no true advantage over standard methods. The technique, known as weak-value amplification, combines a weak transfer of quantum information from system to meter with conditional data rejection, to surprising effect. The Fisher information is a powerful tool for evaluating the performance of any parameter estimation model, and it reveals the technique to be worse than ordinary, preselected only measurements. That this is true despite the presence of noise (including magnetic field fluctuations causing deco- herence, poor resolution detection, and random displacements), casts serious doubt on the utility of the method.

This thesis is concerned with modelling the dynamics of open quantum systems in several different contexts. Of principal interest is the manner in which the environment can modify, or even dominate, a system’s quantum behaviour in order to facilitate the transport of energetic excitations. In the first research chapter, a time-local, non-Markovian quantum master equation is derived in a variationally defined reference frame, for networks of two-level systems coupled to bosonic environments. The predictions of this master equation are then compared with those derived using both weak-coupling and polaron approximations. The variational master equation is found to agree with these standard approaches in their regimes of validity, whilst interpolating between them in intermediate parameter regimes. The second research chapter focusses on the dynamics of a superconducting double quantum dot embedded in a resonant circuit. The device is considered in a regime where the ground state consists of a coherent spatial superposition of a single Cooper pair, which can be excited by a variety of interactions with the environment. The relevant transition rates are calculated and the processes responsible are identified. A numerical simulation of the system is then used to explain experimental data, and show that for certain parameters a significant fraction of excitations occur via absorption of photons from the environment. The final chapter considers a model for an olfactory receptor, in which odorant molecules are recognised by their vibrational modes. Electron transfer occurs in the receptor, dependent on the presence of a vibrational mode of the right frequency. A quantum master equation for the system is derived, and the resulting dynamics is compared to earlier semi-classical treatments. The behaviour of the receptor is found to be sensitive not only to the frequency of the vibrational mode, but also to the character of the surrounding environment. Increased dissipation on the odorant mode, as well as the presence of higher frequencies in the environment is found to improve the frequency resolution of the receptor.

The lack of direct evidence for physics beyond the SM at the LHC has led some to reevaluate the need for such physics to solve the hierarchy problem. Instead, the notion that the SM, or something like it, is valid up to the Planck scale and that technical naturalness is sufficient for solving the hierarchy problem has been suggested. This thesis examines minimal extensions of the SM that address its phenomenological and theoretical shortcomings while avoiding new physics between the electroweak and Planck scales that introduces a hierarchy problem. This thesis first studies two issues with the vMSM - an extension of the SM by three right-handed neutrinos - and their possible solutions. The first issue is the tension between dark matter production in the nuMSM and constraints from the Lyman-alpha forest data. To avoid this tension, the vMSM is extended by a Higgs singlet Φ and neutrino dark matter is produced through the decays of Φ rather than through left-right neutrino mixing. It is shown that the hierarchical parameters of this model can arise from symmetries broken at or near the Planck scale for two specific examples: one in which Φ stabilizes the electroweak vacuum and one in which Φ is a light inflaton. The second issue pertains to Higgs ξ-inflation. In the vMSM, a large non-minimal coupling ξ of the Higgs to gravity gives inflation but leads to a possible violation of perturbative unitarity below the inflationary scale. A study of Higgs ξ-inflation with Mh ≃ 125-126 GeV, for which the Higgs self-coupling λ runs to small values near the Planck scale, is carried out. It is shown that small λ can significantly reduce ξ required for inflation, but ξ cannot be small enough to address the possible unitarity issue. For small λ, a new region of Higgs ξ-inflation with a large tensor-to-scalar ratio r that is consistent with BICEP2 is discovered. This thesis then studies the technical naturalness and cosmology of a model that addresses the strong CP problem. It is shown that a classically scale invariant DFSZ invisible aξon model with a Peccei-Quinn scalar S, whose couplings to the SM are ultra-weak, can solve the strong CP problem and generate electroweak symmetry breaking via the Coleman-Weinberg mechanism. The ultra-weak couplings of S are natural due to an underlying approξmate shift symmetry. The model contains a light pseudo-Goldstone dilaton that can be consistent with cosmological bounds while the aξon can be the dark matter of the universe. Finally, a summary of the thesis is presented and future research topics are suggested.

The striking evidence for the existence of dark matter in the Universe implies that there is new physics to be discovered beyond the Standard Model. To identify the nature of this dark matter is a key task for modern astroparticle physics, and a large number of experiments pursuing a range of different search strategies have been developed to solve it. The topic of this thesis is the complementarity of these different experiments and the issue of how to combine the information from different searches independently of experimental and theoretical uncertainties. The first part focuses on the direct detection of dark matter scattering in nuclear recoil detectors, with a special emphasis on the impact of the assumed velocity distribution of Galactic dark matter particles. By converting experimental data to variables that make the astrophysical unknowns explicit, different experiments can be compared without implicit assumptions concerning the dark matter halo. We extend this framework to include annual modulation signals and apply it to recent experimental hints for dark matter, showing that the tension between these results and constraints from other experiments is independent of astrophysical uncertainties. We explore possible ways of ameliorating this tension by changing our assumptions on the properties of dark matter interactions. In this context, we propose a new approach for inferring the properties of the dark matter particle, which does not require any assumptions about the structure of the dark matter halo. A particularly interesting option is to study dark matter particles that couple differently to protons and neutrons (so-called isospin-violating dark matter). Such isospin-violation arises naturally in models where the vector mediator is the gauge boson of a new U(1) that mixes with the Standard Model gauge bosons. In the second part, we first discuss the case where both the Z' and the dark matter particle have a mass of a few GeV and then turn to the case where the Z' is significantly heavier. While the former case is most strongly constrained by precision measurements from LEP and B-factories, the latter scenario can be probed with great sensitivity at the LHC using monojet and monophoton searches, as well as searches for resonances in dijet, dilepton and diboson final states. Finally, we study models of dark matter where loop contributions are important for a comparison of LHC searches and direct detection experiments. This is the case for dark matter interactions with Yukawa-like couplings to quarks and for interactions that lead to spin-dependent or momentum suppressed scattering cross sections at tree level. We find that including the contribution from heavy-quark loops can significantly alter the conclusions obtained from a tree-level analysis.

This thesis contains a study of topological phases of matter, with a strong emphasis on symmetry as a unifying theme. We take the point of view that the "topology" in many examples of what is loosely termed "topological matter", has its origin in the symmetry data of the system in question. From the fundamental work of Wigner, we know that topology resides not only in the group of symmetries, but also in the cohomological data of projective unitary-antiunitary representations. Furthermore, recent ideas from condensed matter physics highlight the fundamental role of charge-conjugation symmetry. With these as physical motivation, we propose to study the topological features of gapped phases of free fermions through a Z2-graded C*-algebra encoding the symmetry data of their dynamics. In particular, each combination of time reversal and charge conjugation symmetries can be associated with a Clifford algebra. K-theory is intimately related to topology, representation theory, Clifford algebras, and Z2-gradings, so it presents itself as a powerful tool for studying gapped topological phases. Our basic strategy is to use various K

This thesis contains phenomenological studies of top quark production in the forward region of phase space at the Large Hadron Collider (LHC). The production of highly forward top quarks has so far not been observed in nature. As the LHCb detector at the LHC is instrumented in the forward region, this opens the possibility of studying top quark properties in this yet unexplored region of phase space. This feasibility of performing cross section and charge asymmetry measurements of top quark pairs with available and future LHCb data is studied in detail. In both cases, potential analysis strategies are proposed, and sophisticated theoretical predictions are provided for both signal and background. By studying the expected experimental sensitivity of cross section measurements, the potential constraints on parton distribution functions is quantified. The sensitivity of the proposed charge asymmetry measurements with the full Run II LHCb data is also considered.

In this thesis, we study compactifiations of ten-dimensional heterotic supergravity at O(α'), focusing on the moduli of such compactifications. We begin by studying supersymmetric compactifications to four-dimensional maximally symmetric space, commonly referred to as the Strominger system. The compactifications are of the form M10 = M4 x X, where M4 is four-dimensional Minkowski space, and X is a six-dimensional manifold of what we refer to as heterotic SU(3)-structure. We show that this system can be put in terms of a holomorphic operator D on a bundle Q = T* X ⊕ End(TX) ⊕ End(V ) ⊕ TX, defined by a series of extensions. Here V is the E8 x E8 gauge-bundle, and TX is the tangent bundle of the compact space X. We proceed to compute the infinitesimal deformation space of this structure, given by TM = H(0,1)(Q), which constitutes the infinitesimal spectrum of the lower energy four-dimensional theory. In doing so, we find an over counting of moduli by H(0,1)(End(TX)), which can be reinterpreted as O(α') field redefinitions. In the next part of the thesis, we consider non-maximally symmetric compactifications of the form M10 = M3 x Y , where M3 is three-dimensional Minkowski space, and Y is a seven-dimensional non-compact manifold with a G2-structure. We write X → Y → ℝ, where X is a six dimensional compact space of half- at SU(3)-structure, non-trivially fibered over ℝ. These compactifications are known as domain wall compactifications. By focusing on coset compactifications, we show that the compact space X can be endowed with non-trivial torsion, which can be used in a combination with %α'-effects to stabilise all geometric moduli. The domain wall can further be lifted to a maximally symmetric AdS vacuum by inclusion of non-perturbative effects in a heterotic KKLT scenario. Finally, we consider domain wall compactifications where X is a Calabi-Yau. We show that by considering such compactifications, one can evade the usual no-go theorems for flux in Calabi-Yau compactifications, allowing flux to be used as a tool in such compactifications, even when X is Kähler. The ultimate success of these compactifications depends on the possibility of lifting such vacua to maximally symmetric ones by means of e.g. non-perturbative effects.

In this thesis, the response of DNA and RNA to linear and torsional mechanical stress is studied using coarse-grained models. Inspired by single-molecule assays developed over the last two decades, the end-to-end extension, buckling and torque response behaviour of the stressed molecules is probed under conditions similar to experimentally used setups. Direct comparison with experimental data yields excellent agreement for many conditions. Results from coarse-grained simulations are also compared to the predictions of continuum models of linear polymer elasticity. A state diagram for supercoiled DNA as a function of twist and tension is determined. A novel confomational state of mechanically stressed DNA is proposed, consisting of a plectonemic structure with a denaturation bubble localized in its end-loop. The interconversion between this novel state and other, known structural motifs of supercoiled DNA is studied in detail. In particular, the influence of sequence properties on the novel state is investigated. Several possible implications for supercoiled DNA structures in vivo are discussed. Furthermore, the dynamical consequences of coupled denaturation and writhing are studied, and used to explain observations from recent single molecule experiments of DNA strand dynamics. Finally, the denaturation behaviour, topology and dynamics of short DNA minicircles is studies using coarse-grained simulations. Long-range interactions in the denaturation behaviour of the system are observed. These are induced by the topology of the system, and are consistent with results from recent molecular imaging studies. The results from coarse-grained simulations are related to modelling of the same system in all-atom simulations and a local denaturation model of DNA, yielding insight into the applicability of these different modelling approaches to study different processes in nucleic acids.

This thesis considers coarse-grained models of DNA and RNA, developed in particular to study nanotechnological applications as well as some important biophysical processes. We first introduce sequence-dependent thermodynamics into a previously developed coarse-grained rigid base-pair model of DNA. This model is then used to study sequence-dependent effects in multiple DNA systems including: the heterogeneous stacking transition of single strands, the fraying of a duplex, the effects of stacking strength in the loop on the melting temperature of hairpins, the force-extension curve of single strands, and the structure of a kissing-loop complex. We further apply the DNA model to study in detail the properties of an autonomous unidirectionally propagating DNA nanotechnological device, called the ``burnt bridges motor''. We then apply the coarse-graining methods developed for the DNA model to construct a new sequence-dependent coarse-grained model of RNA, which aims to capture basic thermodynamic, structural and mechanical properties of RNA molecules. We test the model by studying its thermodynamics for a variety of secondary structure motifs and also consider the force-extension properties of an RNA duplex. This RNA model allows for efficient simulations of a variety of RNA systems up to hundreds or even thousands of base-pairs. Its versatility is further demonstrated by studying the thermodynamics of a pseudoknot folding, the formation of a kissing loop complex, the structure of a hexagonal RNA nanoring, and the unzipping of a hairpin.

The extended kagome lattice, composed of alternating kagome and triangular layers, provides a novel geometry for frustrated magnetism. In this thesis, we study the properties of Heisenberg spins with nearest-neighbour antiferromagnetic interactions on this lattice. In common with many other models of frustrated magnets, this system has highly degenerate classical ground states. It is set apart from other examples, however, by the strong interlayer correlations between triangular layer spins. We study the implications of such correlations in both the statics and dynamics. We characterise classical ground states using a flux picture for a single layer of kagome spins, a theoretical description that sets geometrical bounds on correlations. We quantify the divergent but sub-extensive ground state degeneracy by a Maxwellian counting argument, and verify this calculation by analysing the energy eigenvalues of numerical ground states. We explore the ground state connectedness but do not reach firm conclusions on this issue. We use the self-consistent Gaussian approximation (SCGA) to calculate static spin correlations at finite temperature. The results of these calculations agree well with elastic neutron scattering experiments. We derive an expression for the effective interlayer interaction between kagome spins by integrating out the triangular lattice spins. We use linear spinwave theory to compute the spin excitation spectrum numerically. This shows encouraging similarity with inelastic neutron scattering data on a single-crystal YBaCo$_4$O$_7$ sample, for a wide range of wavevector and frequency. This agreement shows that our spin model is a reasonable description of the physics, and suggests that this numerical technique might be useful for other geometrically frustrated magnets. We study the dynamics analytically using the stochastic SCGA recently developed for the pyrochlore lattice. For technical reasons, we apply this technique on a related model, the stacked kagome lattice, rather than on the extended kagome lattice itself. From this we find slow relaxation at low temperature, with a rate ~ T2 compared to the faster ~ T scaling for the pyrochlore. Strikingly, in simulations of the dynamics on the extended kagome lattice by numerical integration of the semiclassical equations of motion, we find two different relaxation rates. Kagome layer spins relax more quickly than the triangular layer spins, having ~ T.

Quasi-one-dimensional quantum models are ideal for theoretically exploring the physical phenomena associated with strong correlations. In this thesis we study three examples where strong correlations play an important role in the static or dynamic properties of the system. Firstly, we examine the behaviour of a doped fermionic two-leg ladder in which umklapp interactions are present. Such interactions arise at special band fillings and can be induced by the formation of charge density wave order in an array of two-leg ladders with long-range (three-dimensional) interactions. For the umklapp which arises from the half-filling of one of the bands, we show that the low-energy theory has a number of phases, including a strong coupling regime in which the dominant fluctuations are superconducting in nature. These superconducting fluctuations carry a finite wave vector – they are the one-dimensional analogue of Fulde-Ferrell-Larkin-Ovchinnikov superconductivity. In a second example, we consider a quantum spin model which captures the essential one-dimensional physics of CoNb2O6, a quasi-one-dimensional Ising ferromagnet. Motivated by high-resolution inelastic neutron scattering experiments, we calculate the dynamical structure in the paramagnetic phase and show that a small misalignment of the transverse field can lead to quasi-particle breakdown – a surprising broadening in the single particle mode observed in experiment. Finally, we study the out-of-equilibrium dynamics of a model with tuneable integrability breaking. When integrability is broken by the presence of weak interactions, we show that the system relaxes to a non-thermal state on intermediate time scales, the so-called “prethermalization plateau”. We describe the approximately stationary behaviour in this regime by constructing a generalised Gibbs ensemble with charges deformed to leading order in perturbation theory. Expectation values of these charges are time-independent, but interestingly the charges do not commute with the Hamiltonian to leading order in perturbation theory. Increasing the strength of the integrability breaking interactions leads to behaviour compatible with thermalisation. In each case we use a combination of perturbative analytical calculations and non-perturbative numerical computations to study the problem at hand.

This research introduces an Origami-inspired dynamic spacecraft radiator,capable of adjusting heat rejection in response to orbital variations and extremetemperature fluctuations in lunar environments. The research centers around thesquare twist origami tessellation, an adaptable geometric structure withsignificant potential for revolutionizing radiative heat control in space.The investigative involves simulations of square twist origami tessellation panelsusing vector math and algebra. This study examines both a two-dimensional (2-D), infinitely thin tessellation, and a three-dimensional (3-D), rigidly-foldabletessellation, each characterized by an adjustable closure or actuation angle “φ”.Meticulously analyzed the heat loss characteristics of both the 2D and 3Dradiators over a 180-degree range of actuation.Utilizing Monte Carlo Ray Tracing and the concept of “view factors”, the studyquantifies radiative heat loss, exploring the interplay of emitted, interrupted, andescaped rays as the geometry adapts to various positions. This method allowedfor an in-depth understanding of the changing radiative heat loss behavior asthe tessellation actuates from fully closed to fully deployed. The findings reveal asignificant divergence between the 2D and 3D square twist origami radiators.With an emissivity of 1, the 3D model demonstrated a slower decrease in theratio of escaped to emitted rays (Ψ) as the closure/actuation angle increased,while the 2D model exhibited a more linear decline. This divergence underscoresthe superior radiative heat loss control capabilities of the 2D square twist origamigeometry, offering a promising turndown ratio of 4.42, validating the model’sefficiency and practicality for radiative heat loss control.Further exploration involved both non-rigidly and rigidly foldable radiator models.The non-rigidly foldable geometry, initially a theoretical concept, is realizedthrough 3D modeling and physical prototyping, demonstrating effective foldabilityand radiative heat loss control. The rigidly foldable model, enhanced withsophisticated techniques for increasing 3D height, showed full actuationcapabilities in a physical prototype, confirming its practical application potential.The research also extends to derivative geometries such as “Star Twist”,“Sloped-Edge Twist”, “Octa Twist”, and “Min-core Square Twist”. Extensivesimulations for these geometries are conducted, exploring their potential foradvanced thermal management systems.In conclusion, this research significantly advances the understanding of squaretwist origami geometry in radiative heat loss control. The study highlights thedistinct behavior and advantages of origami-based designs over conventionalradiators, demonstrating efficient thermal management capabilities andadaptability for space exploration. These findings illuminate the path towarddynamic heat rejection in future space missions, powered by origami radiatortechnology, and open avenues for further optimization and enhanced thermalefficiency.

The Standard Model has been precisely tested by a plethora of experiments and has proved extremely successful at describing the fundamental interactions of subatomic particles. Despite this, there are numerous exciting questions motivating the existence of additional physics beyond the Standard Model. In this dissertation, we study a variety of theoretical and data-driven tools for discovering this physics. For theoretical tools, we explore various effective field theories, including those describing: axions mixing with other axions or non-compact scalars, axion interactions with magnetic monopoles, axion strings interacting with massive fermions, CP violating Higgs portal dark matter, scalar triplet and singlet-doublet models as solutions to the CDF-II W mass anomaly, and modifications to Froggatt-Nielsen models for explaining the hierarchy between different flavors of Standard Model Yukawa couplings. Additionally, we investigate machine learning based data-driven tools for precision Top-quark mass measurement and for anomaly detection.

This thesis collects a few of my essays towards understanding representation learning and generalization in neural networks. I focus on the model setting of Bayesian learning and inference, where the problem of deep learning is naturally viewed through the lens of statistical mechanics. First, I consider properties of freshly-initialized deep networks, with all parameters drawn according to Gaussian priors. I provide exact solutions for the marginal prior predictive of networks with isotropic priors and linear or rectified-linear activation functions. I then study the effect of introducing structure to the priors of linear networks from the perspective of random matrix theory. Turning to memorization, I consider how the choice of nonlinear activation function affects the storage capacity of treelike neural networks. Then, we come at last to representation learning. I study the structure of learned representations in Bayesian neural networks at large but finite width, which are amenable to perturbative treatment. I then show how the ability of these networks to generalize when presented with unseen data is affected by representational flexibility, through precise comparison to models with frozen, random representations. In the final portion of this thesis, I bring a geometric perspective to bear on the structure of neural network representations. I first consider how the demand of fast inference shapes optimal representations in recurrent networks. Then, I consider the geometry of representations in deep object classification networks from a Riemannian perspective. In total, this thesis begins to elucidate the structure and function of optimally distributed neural codes in artificial neural networks.

This thesis is dedicated to the study of a prominent class of dark matter (DM) models, in which the DM relic density is linked to the baryon asymmetry, often referred to as Asymmetric Dark Matter (ADM) theories. In ADM the relic density is set by a particle-antiparticle asymmetry, in direct analogue to the baryons. This is partly motivated by the observed proximity of the baryon and DM relic densities Ω_{DM} ≈ 5 Ω_{B}, as this can be explained if the DM and baryon asymmetries are linked. A general requisite of models of ADM is that the vast majority of the symmetric component of the DM number density, the DM-antiDM pairs, must be removed for the asymmetry to set the DM relic density and thus to explain the coincidence of Ω_{DM} and Ω_{B}. However we shall argue that demanding the efficient annihilation of the symmetric component leads to a tension with experimental constraints in a large class of models. In order to satisfy the limits coming from direct detection and colliders searches, it is almost certainly required that the DM be part of a richer hidden sector of interacting states. Subsequently, examples of such extended hidden sectors are constructed and studied, in particular we highlight that the presence of light pseudoscalars can greatly aid in alleviating the experimental bounds and are well motivated from a theoretical stance. Finally, we highlight that self-conjugate DM can be generated from hidden sector particle asymmetries, which can lead to distinct phenomenology. Further, this variant on the ADM scenario can circumvent some of the leading constraints.

I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level (purportedly more accurate and encompassing) model to that of the high-level (purportedly less accurate and encompassing) model that approximately commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular inter-theory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and non-relativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting non-relativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity.

This thesis considers two areas of research in non-equilibrium soft matter at the mesoscale. In the first part we introduce active colloids in the context of active matter and focus on the particular case of phoretic colloids. The general theory of phoresis is presented along with an expression for the phoretic velocity of a colloid and its rotational diffusion in two and three dimensions. We introduce a model for thermally active colloids that absorb light and emit heat and propel through thermophoresis. Using this model we develop the equations of motion for their collective dynamics and consider excluded volume through a lattice gas formalism. Solutions to the thermoattractive collective dynamics are studied in one dimension analytically and numerically. A few numerical results are presented for the collective dynamics in two dimensions. We simulate an unconfined system of thermally active colloids under directed illumination with simple projection based geometric optics. This system self-organises into a comet-like swarm and exhibits a wide range of non- equilibrium phenomena. In the second part we review the background of polymer translocation, including key experiments, theoretical progress and simulation studies. We present, discuss and use a common model to investigate the potential of patterned nanopores for stochastic sensing and identification of polynucleotides and other heteropolymers. Three pore patterns are characterised in terms of the response of a homopolymer with varying attractive affinity. This is extended to simple periodic block co-polymer heterostructures and a model device is proposed and demonstrated with two stochastic sensing algorithms. We find that mul- tiple sequential measurements of the translocation time is sufficient for identification with high accuracy. Motivated by fluctuating biological channels and the prospect of frequency based selectivity we investigate the response of a homopolymer through a pore that has a time dependent geometry. We show that a time dependent mobility can capture many features of the frequency response.

In this thesis we employ string perturbation theory in toroidal orbifold models to study aspects of supersymmetry breaking in type IIB string theory. First, we determine the dependence of physical Yukawa couplings on blow-up moduli in models with D3-branes at orbifold singularities. Blow-up moduli are scalar fields describing the size of small blow-up cycles in the compactification geometry. In models implementing moduli stabilisation these fields can acquire F-terms and break supersymmetry. We examine the moduli-dependence of physical Yukawa couplings at string tree-level by computing disk correlation functions involving a Yukawa interaction of visible sector fields and an arbitrary number of blow-up moduli. We perform the calculation for one blow-up insertion explicitly and find that the correlation function vanishes if the blow-up modulus is associated with a small cycle distant to the visible sector. For more than one blow-up insertion we show that all such correlation functions are exponentially suppressed by the compactification volume. We explain how these results are relevant to suppressing soft terms to scales parametrically below the gravitino mass. Further, we determine corrections to holomorphic Yukawa couplings on D3-branes at an orbifold singularity due to non-perturbative effects such as gaugino condensation on a stack of D7-branes. This can be done by calculating a one-loop threshold correction to the gauge coupling on the D7-branes. We show that, if present, the new contributions to Yukawa couplings are not aligned with the tree-level couplings. As the new Yukawa couplings contribute to soft A-terms they are sources of flavour-changing neutral currents. Last we discuss an effect unrelated to supersymmetry breaking. We show that orbifold models with D3-branes at orbifold singularities can exhibit kinetic mixing of different massless Abelian factors. For this to be possible, the relevant U(1) factors have to be associated with more than one orbifold singularity.

This thesis contributes with a number of topics to the subject of string compactifications, especially in the instance of the E8 × E8 heterotic string theory compactified on smooth Calabi-Yau threefolds. In the first half of the work, I discuss the Hodge plot associated with Calabi-Yau threefolds that are hypersurfaces in toric varieties. The intricate structure of this plot is explained by the existence of certain webs of elliptic-K3 fibrations, whose mirror images are also elliptic-K3 fibrations. Such manifolds arise from reflexive polytopes that can be cut into two parts along slices corresponding to the K3 fiber. Any two half-polytopes over a given slice can be combined into a reflexive polytope. This fact, together with a remarkable relation on the additivity of Hodge numbers, give to the Hodge plot the appearance of a fractal. Moving on, I discuss a different type of web of manifolds, by looking at smooth Z3-quotients of Calabi-Yau three-folds realised as complete intersections in products of projective spaces. Non-simply connected Calabi-Yau three-folds provide an essential ingredient in heterotic string compactifications. Such manifolds are rare in the classical constructions, but they can be obtained as quotients of homotopically trivial Calabi-Yau three-folds by free actions of finite groups. Many of these quotients are connected by conifold transitions. In the second half of the work, I explore an algorithmic approach to constructing E8 × E8 heterotic compactifications using holomorphic and poly-stable sums of line bundles over complete intersection Calabi-Yau three-folds that admit freely acting discrete symmetries. Such Abelian bundles lead to N = 1 supersymmetric GUT theories with gauge group SU(5) × U(4) and matter fields in the 10, ⁻10, ⁻5, 5 and 1 representations of SU(5). The extra U(1) symmetries are generically Green-Schwarz anomalous and, as such, they survive in the low energy theory only as global symmetries. These, in turn, constrain the low energy theory and in many cases forbid the existence of undesired operators, such as dimension four or five proton decay operators. The line bundle construction allows for a systematic computer search resulting in a plethora of models with the exact matter spectrum of the Minimally Supersymmetric Standard Model, one or more pairs of Higgs doublets and no exotic fields charged under the Standard Model group. In the last part of the thesis I focus on the case study of a Calabi-Yau hypersurface embedded in a product of four CP1 spaces, referred to as the tetraquadric manifold. I address the question of the finiteness of the class of consistent and physically viable line bundle models constructed on this manifold. Line bundle sums are part of a moduli space of non-Abelian bundles and they provide an accessible window into this moduli space. I explore the moduli space of heterotic compactifications on the tetraquadric hypersurface around a locus where the vector bundle splits as a direct sum of line bundles, using the monad construction. The monad construction provides a description of poly-stable S(U(4) × U(1))–bundles leading to GUT models with the correct field content in order to induce standard-like models. These deformations represent a class of consistent non-Abelian models that has co-dimension one in Kähler moduli space.

Millions of years of evolution have led to a wealth of highly adapted functional surfaces in nature. Among the most fascinating are superhydrophobic surfaces which are highly water-repellent and shed drops very easily owing to their chemical hydrophobicity combined with micropatterning. Superhydrophobic materials have attracted a lot of attention due to their practical applications as ultra-low friction surfaces for ships and pipes, water harvesters, de-humidifiers and cooling systems. At small length scales, where surface tension dominates over gravity, these surfaces show a wealth of phenomena interesting to physicists, such as directional flow, rolling, and drop bouncing. This thesis focuses on two examples of dynamic drop interactions with micropatterned surfaces and studies them by means of a lattice Boltzmann simulation approach. Inspired by recent experiments, we investigate the phenomenon of the self-propelled bouncing of coalescing droplets. On highly hydrophobic patterned surfaces drop coalescence can lead to an out-of-plane jump of the composite drop. We discuss the importance of energy dissipation to the jumping process and identify an anisotropy of the jumping ability with respect to surface features. We show that Gibbs' pinning is the source of this anisotropy and explain how it leads to the inhibition of coalescence-induced jumping. The second example we study is the novel phenomenon of pancake bouncing. Conventionally, a drop falling onto a superhydrophobic surface spreads due to its inertia, retracts due to its surface tension, and bounces off the surface. Here we explain a different pathway to bouncing that has been observed in recent experiments: A drop may spread upon impact, but leave the surface whilst still in an elongated shape. This new behaviour, which occurs transiently for certain impact and surface parameters, is due to reversible liquid imbibition into the superhydrophobic substrate. We develop a theoretical model and test it on data from experiments and simulations. The theoretical model is used to explain pancake bouncing in detail.

The research presented in this dissertation presents a methodology to experimentally predict and simulate the mechanical behavior of polymers under high strain rate deformation. Specifically, the interplay between the effects of temperature and strain rate on polymer behavior is examined and then used as a tool to help recreate the high rate mechanical response of several different polymers: ranging from rubbers to amorphous polymers to composites. Multiple literature reviews are conducted and presented in this thesis, e.g. experimental mechanics test methods, high rate behavior, time-temperature equivalence, constitutive modeling, and temperature measurement methods. In accordance with mechanical theory, an experimental and analytical protocol in rate- and temperature- dependence was applied to a range of PVC materials ranging in plasticizer contents. Further to this, these PVC materials were modeled with a rubbery model describing the network stress seen in polymer behavior, and an amorphous polymer model to describe PVC low to high rate responses to deformation. This modeling develops insights in the adiabatic nature of high rate response. Time-temperature equivalence, and the temperature rise during adiabatic deformation, are studied and exploited in order to implement a proposed experimental method which simulates the high rate deformation of polymeric materials. The development of an experimental methodology to simulate and predict high rate behavior is presented, applied, and expanded to a range of materials: amorphous polymers (e.g. PVC 20wt% plasticizer, PMMA, PC) and composites (e.g. polymer bonded explosive simulant). The work also presents and highlights the fact that micro to nano-scale imaging may be used in parallel with the simulation method in order to better understand high rate behavior. Furthermore, in result of the studies conducted in this body of work, several novel techniques were developed, or improved upon, and applied to the current research (e.g. additions to time-temperature equivalence, temperature measurement methods at high, moderate, and low strain rates, and a method for measuring the high rate behavior of soft materials).

We study non-equilibrium and strongly-correlated dynamics in two contexts. We begin by analysing quantum many-body systems out of equilibrium through the lens of cold atomic impurities in Bose gases. Such highly-imbalanced mixtures provide a controlled arena for the study of interactions, dissipation, decoherence and transport in a many-body quantum environment. Specifically we investigate the oscillatory dynamics of a trapped and initially highly-localised impurity interacting with a weakly-interacting trapped quasi low-dimensional Bose gas. This relates to and goes beyond a recent experiment by the Inguscio group in Florence. We witness a delicate interplay between the self-trapping of the impurity and the inhomogeneity of the Bose gas, and describe the dissipation of the energy of the impurity through phononic excitations of the Bose gas. We then study the transport of a driven, periodically-trapped impurity through a quasi one-dimensional Bose gas. We show that placing the weakly-interacting Bose gas in a separate periodic potential leads to a phononic excitation spectrum that closely mimics those in solid state systems. As a result we show that the impurity-Bose gas system exhibits phonon-induced resonances in the impurity current that were predicted to occur in solids decades ago but never clearly observed. Following this, allowing the bosons to interact strongly, we predict the effect of different strongly-correlated phases of the Bose gas on the motion of the impurity. We show that, by observing the impurity, properties of the excitation spectrum of the Bose gas, e.g., gap and bandwidth, may be inferred along with the filling of the bosonic lattice. In other words the impurity acts as a probe of its environment. To describe the dynamics of such a strongly-correlated system we use the powerful and near-exact time-evolving block decimation (TEBD) method, which we describe in detail. The second part of this thesis then analyses, for the first time, the performance of this method when applied to simulate non-equilibrium classical stochastic processes. We study its efficacy for a well-understood model of transport, the totally-asymmetric exclusion process, and find it to be accurate. Next, motivated by the inefficiency of sampling-based numerical methods for high variance observables we adapt and apply TEBD to simulate a path-dependent observable whose variance increases exponentially with system size. Specifically we calculate the expected value of the exponential of the work done by a varying magnetic field on a one-dimensional Ising model undergoing Glauber dynamics. We confirm using Jarzynski's equality that the TEBD method remains accurate and efficient. Therefore TEBD and related methods complement and challenge the usual Monte Carlo-based simulators of non-equilibrium stochastic processes.

We study the low-temperature physics arising in models of a strongly correlated, tunnel-coupled double quantum dot (DQD), particularly the two-impurity Anderson model (2AIM) and the two-impurity Kondo model (2IKM), employing a combination of physical arguments and the Numerical Renormalisation Group. These models exhibit a rich range of Kondo physics. In the regime with essentially one electron on each dot, there is a competition between the Kondo effect and the interdot exchange interaction. This competition gives rise to a quantum phase transition (QPT) between local singlet and Kondo singlet phases in the 2IKM, which becomes a continuous crossover in the 2AIM as a result of the interlead charge transfer present. The 2IKM is known to exhibit two-channel Kondo (2CK) physics at the QPT, and we investigate whether this is also the case for the 2AIM at the crossover. We find that while in principle 2CK physics can be observed in the 2AIM, extremely low temperatures are required, such that it is unlikely that 2CK physics will be observed in an experimental DQD system in the near future. We have studied the effect of a magnetic field on the 2AIM and the 2IKM, finding that both the zero-field QPT in the 2IKM and the zero-field crossover in the 2AIM, persist to finite field. This presents the possibility of observing 2CK physics in an experimental DQD at finite field, but we find that the temperatures required to do so are extremely low. We show that longer even-numbered chains of spins also exhibit QPTs at finite field, and argue that a 2N-spin chain should undergo N QPTs as field is increased (starting deep in the local singlet phase at zero field). We have also carried out a joint theoretical-experimental study of a carbon nanotube based DQD, in collaboration with Dr. Mark Buitelaar et al. The agreement between experimental and theoretical results is good, and the experiments are able to access the crossover present in the 2AIM at finite field. Furthermore, the experiments show the wide range of physics exhibited by DQD systems, and illustrate the utility of such systems in probing correlated electron physics.

Issues of control and causation are central to the Quantum Theory of Computation. Yet there is no place for them in fundamental laws of Physics when expressed in the prevailing conception, i.e., in terms of initial conditions and laws of motion. This thesis aims at arguing that Constructor Theory, recently proposed by David Deutsch to generalise the quantum theory of computation, is a candidate to provide a theory of control and causation within Physics. To this end, I shall present a physical theory of information that is formulated solely in constructor-theoretic terms, i.e., in terms of which transformations of physical systems are possible and which are impossible. This theory solves the circularity at the foundations of existing information theory; it provides a unifying relation between classical and quantum information, revealing the single property underlying the most distinctive phenomena associated with the latter: the unpredictability of the outcomes of some deterministic processes, the lack of distinguishability of some states, the irreducible perturbation caused by measurement and the existence of locally inaccessible information in composite systems (entanglement). This thesis also aims to investigate the restrictions that quantum theory imposes on copying-like tasks. To this end, I will propose a unifying, picture-independent formulation of the no-cloning theorem. I will also discuss a protocol to accomplish the closely related task of transferring perfectly a quantum state along a spin chain, in the presence of systematic errors. Furthermore, I will address the problem of whether self-replication (as it occurs in living organisms) is compatible with Quantum Mechanics. Some physicists, notably Wigner, have argued that this logic is in fact forbidden by Quantum Mechanics, thus claiming that the latter is not a universal theory. I shall prove that those claims are invalid and that the logic of self-replication is, of course, compatible with Quantum Mechanics.

Non-locality and contextuality are key features of quantum mechanics that distinguish it from classical physics. We aim to develop a deeper, more structural understanding of these phenomena, underpinned by robust and elegant mathematical theory with a view to providing clarity and new perspectives on conceptual and foundational issues. A general framework for logical non-locality is introduced and used to prove that 'Hardy's paradox' is complete for logical non-locality in all (2,2,l) and (2,k,2) Bell scenarios, a consequence of which is that Bell states are the only entangled two-qubit states that are not logically non-local, and that Hardy non-locality can be witnessed with certainty in a tripartite quantum system. A number of developments of the unified sheaf-theoretic approach to non-locality and contextuality are considered, including the first application of cohomology as a tool for studying the phenomena: we find cohomological witnesses corresponding to many of the classic no-go results, and completely characterise contextuality for large families of Kochen-Specker-like models. A connection with the problem of the existence of perfect matchings in k-uniform hypergraphs is explored, leading to new results on the complexity of deciding contextuality. A refinement of the sheaf-theoretic approach is found that captures partial approximations to locality/non-contextuality and can allow Bell models to be constructed from models of more general kinds which are equivalent in terms of non-locality/contextuality. Progress is made on bringing recent results on the nature of the wavefunction within the scope of the logical and sheaf-theoretic methods. Computational tools are developed for quantifying contextuality and finding generalised Bell inequalities for any measurement scenario which complement the research programme. This also leads to a proof that local ontological models with `negative probabilities' generate the no-signalling polytopes for all Bell scenarios.

Black hole jets and accretion discs are the most extreme objects in modern astrophysics whilst dark energy is undoubtedly the most mysterious. This thesis focuses on understanding these three topics. The majority of this thesis is dedicated to investigating the structure and properties of black hole jets by modelling their emission. I develop an inhomogeneous jet model with a magnetically dominated parabolic accelerating base, transitioning to a slowly decelerating conical jet, with a geometry set by radio observations of M87. This model is able to reproduce the simultaneous multiwavelength spectra of all 38 Fermi blazars with redshifts in unprecendented detail across all wavelengths. I constrain the synchrotron bright region of the jet to occur outside the BLR and dusty torus for FSRQs using the optically thick to thin synchrotron break. At these large distances their inverse-Compton emission originates from scattering CMB photons. I find an approximately linear relation between the jet power and the transition region radius where the jet first comes into equipartition, transitions from parabolic to conical and stops accelerating. The decreasing magnetic field strength and increasing bulk Lorentz factor with jet power are the physical reasons behind the blazar sequence. I calculate the conditions for instability in a thin accretion disc with an α parameter which depends on the magnetic Prandtl number, as suggested by MHD simulations. The global behaviour of the instability induces cyclic flaring in the inner regions of the disc, for parameters appropriate for X-ray binary systems, thereby offering a potential solution to a long standing problem. Finally, I calculate the effect of an interacting quintessence model of dark energy on cosmological observables. I find that a scalar-tensor type interaction in the dark sector results in an observable increase in the matter power spectrum and integrated Sachs-Wolfe effect at horizon scales.

In this thesis, applications of Holography in the context of Condensed Matter Physics and in particular hydrodynamics, will be studied. Holog- raphy or gauge/gravity duality has been an enormously useful tool in studying strongly-coupled Field Theories with particular success in their low-frequency and large-wavelength fluctuation regime, i.e the hydrody- namical regime. Here, following a phenomenological approach, gravita- tional systems, simple enough to be properly examined, will be studied in order to derive as much information as possible about their dual theories, given that their exact form is not accessible in this way. After a review of the most important elements of standard Condensed Matter Theory, the gauge/gravity duality itself will be presented, along with some of its most important achievements. Having established the framework of this work, the main results of this thesis will be presented. Initially the sound channel of the theory dual to the anti-de Sitter Reissner–Nordstro ̈m black hole space-time will be studied, at finite temperature and finite chemical potential. Hydrodynamical properties of the boundary theory will be of major interest. Following that, focus will be shifted towards another grav- itational system, namely the Electron Star. There, the shear channel of the dual theory will be mainly examined. The goal will be, as before, to extract information about the hydrodynamical properties of the boundary theory.

Understanding the apparent accelerating expansion rate of the universe is a challenge for modern cosmology. One category of explanations is that we are using the wrong gravitational physics to study the observations. Our paradigmatic theory of gravity – Einstein’s theory of General Relativity – may be subsumed by a larger theory. This thesis develops a selection of tools for testing General Relativity and the numerous alternative theories of gravity that have been put forward. I advocate that an elegant and efficient way to test this space of theories is through the use of parameterized frameworks. Inspired by the Parameterized Post-Newtonian framework I develop a new formalism, the Parameterized Post-Friedmann formalism, that aims to unify the linear cosmological perturbation theory of many alternatives to General Relativity. Having introduced the Parameterized Post-Friedmann formalism and demonstrated its application via a suite of examples, I examine several issues surrounding parameterized tests of gravity. I first consider how the structure of a parameterization can influence the constraints obtainable from a given set of data. I then consider how to describe the growth of the large-scale structure of the universe in a parameterized manner. This leads to a convenient tool for calculating corrections to the growth rate of structure in modified theories, which can be used both with the Parameterized Post-Friedmann formalism or independently of it. I present forecasts for how well generalized deviations from General Relativity will be constrained by the next generation of galaxy surveys. Throughout, this thesis aims to take a synoptic approach to theories of modified gravity, rather than focussing on specific models. A question yet to be answered is whether this approach is realistic in practical terms. The final part of this thesis takes the first steps towards an answer.

The phenomenon of scale dependent spectral dimension has attracted special interest in the quantum gravity community over the last eight years. It was first observed in computer simulations of the causal dynamical triangulation (CDT) approach to quantum gravity and refers to the reduction of the spectral dimension from 4 at classical scales to 2 at short distances. Thereafter several authors confirmed a similar result from different approaches to quantum gravity. Despite the contribution from different approaches, no analytical model was proposed to explain the numerical results as the continuum limit of CDT. In this thesis we introduce graph ensembles as toy models of CDT and show that both the continuum limit and a scale dependent spectral dimension can be defined rigorously. First we focus on a simple graph ensemble, the random comb. It does not have any dynamics from the gravity point of view, but serves as an instructive toy model to introduce the characteristic scale of the graph, study the continuum limit and define the scale dependent spectral dimension. Having defined the continuum limit, we study the reduction of the spectral dimension on more realistic toy models, the multigraph ensembles, which serve as a radial approximation of CDT. We focus on the (recurrent) multigraph approximation of the two-dimensional CDT whose ensemble measure is analytically controlled. The latter comes from the critical Galton-Watson process conditioned on non-extinction. Next we turn our attention to transient multigraph ensembles, corresponding to higher-dimensional CDT. Firstly we study their fractal properties and secondly calculate the scale dependent spectral dimension and compare it to computer simulations. We comment further on the relation between Horava-Lifshitz gravity, asymptotic safety, multifractional spacetimes and CDT-like models.

This thesis presents a complete theoretical framework for turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding order-by- order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gra- dients in the equilibrium quantities, and the transport-timescale evolu- tion of mean profiles of these quantities driven by the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the high-flow gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local cascade of free energy. Transport equations for the evolution of the mean density, temperature and flow ve- locity profiles are derived. These transport equations show how the neo- classical corrections and the fluctuations act back upon the mean profiles through fluxes and heating. This framework is further developed by exploiting the scale separation between ions and the electrons. The gyrokinetic equation is expanded in powers of the electron to ion mass ratio, which provides a rigorous method for deriving the electron response to ion-scale turbulence. We prove that such turbulence cannot change the magnetic topology, and ar- gue that, therefore, the magnetic field lies on fluctuating flux surfaces. These flux surfaces are used to construct magnetic coordinates, and in these coordinates a closed system of equations for the electron response is derived. All fast electron timescales have been eliminated from these equations. Simplified transport equations for electrons in this limit are also derived.

Scattering amplitudes are fundamental and remarkably rich observables in quantum field theory. The basic observation that makes scattering amplitudes fascinating is that in theories with massless particles of spin s ≥ 1, they are much simpler than might be expected from traditional Feynman diagram techniques for computing them. This simple observation might ultimately have profound consequences for our view of quantum field theory. The broad aim of this thesis is to understand and exploit the hidden simplicity and structure in scattering amplitudes. The quantum field theory with the simplest scattering amplitudes in four dimensions is planar = 4 supersymmetric Yang-Mills theory. This theory has provided considerable inspiration in developing new computational techniques and has provided many important theoretical insights. In this theory, there is a remarkable correspondence between scattering amplitudes and null polygonal Wilson loops, observables which on first inspection look very different. In this thesis, we will provide new insights into this correspondence using methods from twistor theory and exploit the symmetries of the problem to find new ways of computing scattering amplitudes.

In this thesis, we consider heterotic string vacua based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold preserving only two supercharges. Thus, they correspond to half-BPS states of heterotic supergravity. The constraints on the internal manifolds with $SU(3)$ structure are derived. They are found to be a generalization of half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that heterotic compactifications on half-flat mirror manifolds are based on this class of solutions. Furthermore, within this context, we construct specific examples based on six-dimensional nearly-Kahler homogeneous manifolds and non-trivial vector bundles thereon. Our solutions are based on three specific group coset spaces satisfying the half-flat torsion class conditions. It is shown how to construct line bundles over these manifolds, compute their properties and build up vector bundles consistent with supersymmetry and the heterotic anomaly cancellation. It turns out that the most interesting solutions are obtained from SU(3)/U(1)². This space supports a large number of vector bundles leading to consistent heterotic vacua with GUT group and, for some of them, with three chiral families.

This thesis studies the cosmology of ultra-light scalar fields with masses in the range 10−33 eV ? m ? 10−18 eV and their effects on cosmology. The existence of such fields is motivated by the theoretical framework of the "String Axiverse". All types of string theory contain multiple axion fields associated with antisymmetric tensor fields compactified on closed cycles in the compact space. Since the masses of these fields scale exponentially with the volume of the cycle, it is possible for them to be naturally light. We study the effects of these fields as a component of the dark matter and show analytically and numerically that they cause a suppression of structure formation on cosmological scales set by the inverse mass. We show that it will be possible with future galaxy redshift and weak lensing surveys to detect an ultra- light field comprising of order a percent of the total dark matter. If such a field is allowed to couple to the geometry that provided its mass via a phenomenological scalar potential for the axion and modulus, then the expansion of the universe can be altered significantly. In particular, we find that it is possible to have multiple epochs of accelerated expansion over a large region of parameter space, and to have a flat universe with a big crunch in the distant future. Finally, we address the issue of isocurvature perturbations in axion cosmologies, and demonstrate that in the ultra-light case the power spectrum is effected. This may have implications for the conclusions made about fine tuning in the axiverse in relation to a potential detection of tensor modes in the CMB that are different to the case of a standard axion.

The thesis commences with a detailed review of the background theory of spin dynamics simulations. State space restriction is introduced via a "top-down" approach. Common terms that make up the spin Hamiltonian are reviewed, and it is noted that the mathematical forms of these terms can be categorised in one of three ways. The review of the background theory complete, accounts are given of the following four areas of research: 1. Formal conditions are established for the validity of state space restriction via spin order pruning, based on tracking the density matrix norm through spin order subspaces. The primary predictor for success is seen to be the ratio of the largest eigenvalue to the relaxation rate. The lower this ratio, the fewer spin orders are required. 2. Software based around the Spin XML format, suitable for constructing and visualising large spin systems, is presented. Both a functional specification and a discussion of the internals are given. 3. A potential application of state space restriction, called "direct structure fitting", (DSF) is explored. In DSF, a candidate chemical structure is optimised directly by minimising the difference between its predicted spectrum and an experimental spectrum. The following examples of successful fits are provided: cyanomethyl, propargyl, and tyrosyl radicals, in the liquid state, and, tyrosyl embedded in two ribonuclease reductase proteins in the powder state. 4. A new model of the pseudocontact shift, which assumes a delocalised electron, is presented. Mathematical subtleties are resolved that would otherwise lead to the failure of numerical evaluation if left untreated. Techniques to improve efficiency are discussed, and the resulting program runs comfortably on workstation-grade hardware on protein sized datasets. E. Coli DNA Polymerase III is investigated as an example, and evidence is presented that suggests that the new model would predict significant differences in structures if used in conjunction with molecular dynamics based structural refinement.

We present original calculations of standard model processes involving two weak bosons at NLO in QCD, and study related phenomenology with reference to Higgs boson and new physics searches at the LHC. We employ a new theoretical technique, D-dimensional generalised unitarity, to obtain the multi-particle, one-loop scattering amplitudes for the processes pp → W+W- + 1j, pp → W+W- + 2j, pp → W+W+ + 2j, and gg → W+W-g. We consider the LHC phenomenology of: the W+W- + n jets background to Higgs searches, for n = 0,1,2; the effects of anomalous tri-linear gauge couplings in WW and WZ production; the background W+W+ + 2j to new physics searches involving like-sign leptons; and a method of spin determination of new states in a scenario where conventional methods fail.

Evolutionary dynamics arise from the interplay of mutation and selection. Fundamentally, these two processes operate at different levels: Mutations modify genetic information (the genotype), which is passed from parent to offspring. Selection is triggered by variation in reproductive success, which depends on the physical properties (the phenotype) of an organism and its environment. Thus the genotype-phenotype map determines if and how mutations can lead to selection. The aim of this dissertation is to incorporate this map explicitly into a theoretical description of evolutionary dynamics. The first part of the analysis presented here is concerned with the static properties of simple models of these maps, which are studied using exhaustive enumeration. The two most important observations are phenotypic bias – some phenotypes are realized by many more genotypes than most other phenotypes – and the existence of neutral spaces – genotypes with the same phenotype can often be reached from each other by single mutational steps. The remainder of the dissertation provides a theoretical description of evolutionary dynamics on and across neutral spaces. Two different mean-field approximations lead to simple analytic results for the first discovery of alternative phenotypes, highlighting the importance of phenotypic bias: Rare phenotypes are hard to find by evolutionary search. These results are used to discuss the relationship of robustness, the ability to withstand mutational change, and evolvability, the ability to create variation through mutation. Several types of fluctuations beyond the mean-field limit are studied, both theoretically and in simulations. The discrete structure of genotype spaces can lead to strong correlations in the spectra of phenotypes produced, increasing the probability that a particular phenotype is fixed in the population quickly after its discovery. Structural correlations between genotypes can increase the effect of phenotypic bias, while the qualitative features of the mean-field description remain valid. All these results highlight that neutral spaces impact evolutionary dynamics in many non-trivial ways, in particular by favouring phenotypes of high accessibly, but comparably low fitness over those phenotypes that are highly fit, but very hard to discover.

In this thesis we review the gauge/gravity duality and how it can be used to compute the thermodynamic properties and low-energy excitations of holographic quantum liquids - strongly-interacting field theories with a non-zero density of matter. We then study in detail the charge density excitations of two such liquids, the D3/D7 theory and the RN-AdS₄ theory, by computing the poles of their charge density Green's functions, and their charge density spectral functions. Although it is not a Landau Fermi liquid, the charge density excitations of the D3/D7 theory display many of the same properties as one, including a collisionless/hydrodynamic crossover as the temperature is increased. In contrast to this, the charge density (and energy density) excitations of the RN-AdS₄ theory do not share these properties but behave in a way that cannot be explained by Landau's theory of interacting fermionic quasiparticles. This is consistent with other results which indicate that this is not a Landau Fermi liquid.

Hadronic collider experiments have played a major role in particle physics phenomenology over the last few decades. Data recorded at the Tevatron at Fermilab is still of interest, and its successor, the Large Hadron Collider (LHC) at CERN, has recently announced the discovery of a particle consistent with the Standard Model Higgs boson. Hadronic colliders look set to guide the field for the next fifteen years or more, with the discovery of more particles anticipated. The discovery and detailed study of new particles relies crucially on the availability of high-precision theoretical predictions for both the signal and background processes. This requires observables to be calculated to next-to-leading order (NLO) in perturbative quantum chromodynamics (QCD). Many hadroproduction processes of interest contain multiple particles in the final state. Until recently, this caused a bottleneck in NLO QCD calculations, due to the difficulty in calculating one-loop corrections to processes involving three or more final state particles. Spectacular developments in on-shell methods over the last six years have made these calculations feasible, allowing highly accurate predictions for final state observables at the Tevatron and LHC. A particular realisation of on-shell methods, generalised unitarity, is used to compute the NLO QCD cross-sections and distributions for two processes: the hadroproduction of W+ W-jj, and the hadroproduction of W+ W-jj. The NLO corrections to both processes serve to reduce the scale dependence of the results significantly, while having a moderate effect on the central scale choice cross-sections, and leaving the shapes of the kinematic distributions mostly unchanged. Additionally, the gluon fusion contribution to the next-to-next-to-leading order (NNLO) QCD corrections to W+ W-j productions are studied. These contributions are found to be highly depen- dent on the kinematic cuts used. For cuts used in Higgs searches, the gluon fusion effect can be as large as the NLO scale uncertainty, and should not be neglected. All of the higher-order QCD corrections increase the accuracy and reliability of the theoretical predictions at hadronic colliders.

Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to perform. In the first part of this thesis we quantify the effective entanglement when operations are additionally restricted to account for both fundamental restrictions on operations, such as those arising from superselection rules, as well as experimental errors arising from the imperfections in the apparatus. For an important class of errors we find a linear relationship between the usual and effective higher dimensional generalization of concurrence, a measure of entanglement. Following the treatment of effective entanglement, we focus on a related concept of nonlocality in the presence of superselection rules (SSR). Here we propose a scheme that may be used to activate nongenuinely multipartite nonlocality, in that a single copy of a state is not multipartite nonlocal, while two or more copies exhibit nongenuinely multipartite nonlocality. The states used exhibit the more powerful genuinely multipartite nonlocality when SSR are not enforced, but not when they are, raising the question of what is needed for genuinely multipartite nonlocality. We show that whenever the number of particles is insufficient, the degrading of genuinely multipartite to nongenuinely multipartite nonlocality is necessary. While in the first few chapters we focus our attention on understanding the resources present in quantum states, in the final part we turn the picture around and instead treat operations themselves as a resource. We provide our observers with free access to classical operations - ie. those that cannot detect or generate quantum coherence. We show that the operation of interest can then be used to either generate or detect quantum coherence if and only if it violates a particular commutation relation. Using the relative entropy, the commutation relation provides us with a measure of nonclassicality of operations. We show that the measure is a sum of two contributions, the generating power and the distinguishing power, each of which is separately an essential ingredient in quantum communication and information processing. The measure also sheds light on the operational meaning of quantum discord - we show it can be interpreted as the difference in superdense coding capacity between a quantum state and a classical state.

Turbulence is a major factor limiting the achievement of better tokamak performance as it enhances the transport of particles, momentum and heat which hinders the foremost objective of tokamaks. Hence, understanding and possibly being able to control turbulence in tokamaks is of paramount importance, not to mention our intellectual curiosity of it. We take the first step by making measurements of turbulence using the 2D ($8$ radial $imes$ $4$ poloidal channels) beam emission spectroscopy (BES) system on the Mega Amp Spherical Tokamak (MAST). Measured raw data are statistically processed, generating spatio-temporal correlation functions to obtain the physical characteristics of the turbulence such as spatial and temporal correlation lengths as well as its motion. The reliability of statistical techniques employed in this work is examined by generating and utilizing synthetic 2D BES data. The apparent poloidal velocity of fluctuating density patterns is estimated using the cross-correlation time delay method. The experimental results indicate that the poloidal motion of fluctuating density patterns in the lab frame arises because the patterns are advected by the strong toroidal plasma flows while the patterns are aligned with the background magnetic fields which are not parallel to the flows. Furthermore, various time scales associated with the turbulence are calculated using statistically estimated spatial correlation lengths and correlation times of turbulence. We find that turbulence correlation time, the drift time associated with ion temperature or density gradients, the ion streaming time along the magnetic field line and the magnetic drift time are comparable and possibly scale together suggesting that the turbulence, determined by the local equilibrium, is critically balanced. Finally, we argue that we have produced a critical manifold in the experimentally obtained local equilibrium parameter space separating dominant turbulent transport from a non-turbulent or weakly turbulent state. It shows that the inverse ion-temperature-gradient scale length is correlated inversely with $q/arepsilon$ (safety factor/inverse aspect ratio) and positively with the plasma rotational shear. Practically, this means that we can attain the stiffer ion-temperature-gradient, thus hotter plasma core, without increasing the rotational shear.

This Thesis studies some aspects of string compactifications with particular em- phasis on moduli stabilisation and cosmology. In Chapter 1 I motivate the study of string compactifications as a way to build on the successes of the Standard Model of Particle Physics and of the theory of General Relativity. Chapter 2 constitutes an overview of the technical background necessary for the study of flux compactifications. I sketch how the desire to obtain a supersymmet- ric theory in four dimensions constrains us to consider compactifications of the ten dimensional theory in six dimensional Calabi-Yau orientifolds. I argue that it is strictly necessary to stabilise the geometry of this compact space in order to have a phenomenologically viable four dimensional theory. I introduce the large volume scenario of type IIB compactifications that successfully incorporates fluxes and sub- leading corrections to yield a four dimensional theory with broken supersymmetry and all geometrical moduli stabilised. The next four Chapters are devoted to the study of some phenomenological aspects of moduli stabilisation and constitute the original work developed for this Thesis. In Chapter 3 I investigate the consequences of field redefinitions in the stabilisation of moduli and supersymmetry breaking, finding that redefinitions of the small blow- up moduli do not significantly alter the standard picture of moduli stabilisation in the large volume scenario and that the soft supersymmetry breaking terms are generated at the scale of the gravitino mass. Chapter 4 deals with the putative destabilisation of the volume modulus by very dense objects. The analysis of the moduli potential shows that even the densest astrophysical objects cannot destabilise the moduli, and that destabilisation is only achievable in the context of black hole formation and cosmological singularities. In Chapter 5 I present a model of inflation within the large volume scenario. The inflaton is identified with a geometric modulus, the fibre modulus, and its potential generated by poly-instanton effects. The model is shown to be robust and consistent with current observational constraints. In Chapter 6 I introduce a model of quintessence, where the quintessence field and its potential share the same origin with the inflationary model of the previous Chapter. This model constitutes a stringy realisation of supersymmetric large extra dimensions, where supersymmetry, the low gravity scale and the scale of dark energy are intrinsically connected. I conclude in Chapter 7 outlining the direction of future research.

Categorical quantum mechanics is a way of formalising the structural features of quantum theory using category theory. It uses compound systems as the primitive notion, which is formalised by using symmetric monoidal categories. This leads to an elegant formalism for describing quantum protocols such as quantum teleportation. In particular, categorical quantum mechanics provides a graphical calculus that exposes the information flow of such protocols in an intuitive way. However, the graphical calculus also reveals surprising features of these protocols; for example, in the quantum teleportation protocol, information appears to flow `backwards-in-time'. This leads to question of how causal structure can be described within categorical quantum mechanics, and how this might lead to insight regarding the structural compatibility between quantum theory and relativity. This thesis is concerned with the project of formalising causal structure in categorical quantum mechanics. We begin by studying an abstract view of Bell-type experiments, as described by `no-signalling boxes', and we show that under time-reversal no-signalling boxes generically become signalling. This conflicts with the underlying symmetry of relativistic causal structure. This leads us to consider the framework of categorical quantum mechanics from the perspective of relativistic causal structure. We derive the properties that a symmetric monoidal category must satisfy in order to describe systems in such a background causal structure. We use these properties to define a new type of category, and this provides a formal framework for describing protocols in spacetime. We explore this new structure, showing how it leads to an understanding of the counter-intuitive information flow of protocols in categorical quantum mechanics. We then find that the formal properties of our new structure are naturally related to axioms for reconstructing quantum theory, and we show how a reconstruction scheme based on purification can be formalised using the structures of categorical quantum mechanics. Finally, we discuss the philosophical aspects of using category theory to describe fundamental physics. We consider a recent argument that category-theoretic formulations of physics, such as categorical quantum mechanics, can be used to support a variant of structural realism. We argue against this claim. The work of this thesis suggests instead that the philosophy of categorical quantum mechanics is subtler than either operationalism or realism.

An active particle converts energy to motion. An active suspension is a population of active particles, typically microscale, that are immersed in a viscous and/or elastic medium. This thesis is about the statistics of active suspensions. Unlike a suspension at thermodynamic equilibrium, we show that an active suspension inherently has non-Gaussian fluctuations due to an interplay between self-driven constituents and microscopic physics. Consequently, the diffusion of a tracer in an active suspension is not Gaussian. Our results explain some experiments with active suspensions that contain either swimming microorganisms or molecular motors. We provide different models for the fluctuations in dilute active suspensions, ranging from phenomenological to exact. The fundamental ingredient of such non-Gaussian fluctuations is an ultraslow convergence to the central limit theorem caused by truncated power-laws. Without any truncation, there is an intimate relation to the generalized central limit theorem. We suggest similar effects occur in many other systems. These may be associated with probability distributions that appear to be exponential.