Non-contact atomic force microscopy allows us to directly probe the interactions between atoms and molecules. When operated in UHV and at low temperatures, a host of experiments, uniquely possible with the technique, can be carried out. The AFM allows us to characterise the forces present on a surface, resolve the atomic structure of molecules, measure the force required to move an atom, and even directly measure molecular pair potentials. Generally speaking, it is the interaction between the outermost tip and surface atoms that we measure. Therefore, in each of these experiments, understanding, or controlling, the tip termination is essential. As NC-AFM experiments become increasingly sophisticated, the combination of experiment and simulation has become critical to understand, and guide the processes at play. In this thesis, I focus on semiconductor surfaces and investigate the role of tip structure in a variety of situations with both DFT simulations and NC-AFM experiments. The clean Si(100) surface consists of rows of dimers, which can be manipulated between two different states using an NC-AFM. In order to understand the manipulation process, detailed DFT and NEB simulations were conducted to examine the energy balance of ideal and defective surfaces, with or without the presence of an AFM tip. We show that an explanation can only be reached when we consider both the AFM tip and variations in the PES caused by surface defects. NC-AFM experiments were also conducted on Si(100):H. We find that on this surface we regularly cultivate chemically passivated, hydrogen-terminated, tip apices which lead to distinct inverted image contrasts in our AFM images. Following a thorough characterisation of the tip apex, we conduct preliminary experiments designed to investigate surface defect structures, and to chemically modify the tip termination. Detailed DFT simulations show that this type of tip engineering, however, critically depends on the larger tip structure, significantly complicating the chances of success. Additionally, we investigate the structure and stability of silicon tip apices using DFT. Even with relatively simple tip structures, we observe complex behaviours, such as tip-dependent dissipation and structural development. These processes provide interesting information regarding tip stability, and commonly observed experimental behaviour. We also model an experiment in which we functionalise the tip apex with a C60 molecule, revealing for the first time that submolecular resolution is possible in the attractive regime.

This thesis is devoted to the study of modified gravity theories, especially, the scalar-tensor theories. A theorem due to Weinberg which states, that the equivalence principle is a necessary consequence of Lorentz invariance in a gravitational theory described by spin-2 massless particles is presented in Chapter 2. In view of this theorem modified gravity models either attempt to make \textit{graviton} massive or add other spin degrees of freedom. Scalar tensor theories are a simple and natural choice. An overview of some important scalar-tensor theories such as, Brans-Dicke model, DGP theory (although not a scalar-tensor theory it reduces to one in the so called \textit{decoupling} limit as we would see in chapter 2), Galileon model, Horndeski theory is also given in Chapter 2. The Hamiltonian analysis of the Galileon model is presented in Chapter 3. Chapter 4 presents the boundary terms and junction conditions of the Horndeski theory in the presence of codimension-1 branes. A generalised multiple-scalar-tensor theory analogous to Horndeski theory is developed in Chapter 5. We conclude with the proof of the most general multiple scalar field theory in arbitrary dimensions and flat-space time in Chapter 6. Chapters 3,4,5,6 are original work where the first 3 are based on the following journal articles.

Atom chips are a great tool for creation of low dimensional magnetic trapping geometries via micro-structures on the chip surface. Such structures allow the creation of time-dependent magnetic and electric potentials with highly accurate spatial and temporal dependency. As part of this thesis we have investigated the coherence dynamics in one-dimensional Bose-Einstein condensate while creating a sudden change in the atomic trapping potential. Such sudden changes create phase perturbations of the wave function, which leads to density perturbations. Analyzing these changes enables studies of the evolution of the coherence in a one-dimensional Bose gas with dynamically changing boundary conditions. Of particular interest is the study of prethermalization which can be understood in an integrable systems as so-called generalized Gibbs state. This state does not decay, but in case that there are perturbations that break integrability, this state relaxes further to a thermal state. To get a good understanding of such 1D systems we first investigated the transition from 3D to 1D Bose gas by observing both in situ and time of flight density profiles and analyzing the spatial variations in atom number as a function of temperature, geometry, and atomic density. High quality imaging is essential in these types of atomic physics experiments, and therefore a whole chapter is devoted to a new optimization method of absorption imaging. In this method we have taken into account the quantum nature of both the atomic medium and imaging light. Last, we have outlined an experiment that utilizes one-dimensional Bose-Einstein condensate as an analogue model of quantum field theory, in particular the dynamical Casimir effect and Hawking radiation. We do so by dynamically splitting a condensate along its long axis to a Y-like shape and measure the differential phase between the branches.

In this thesis two single molecule magnets based on the dodecamanganese (III, IV) cluster, with either benzoate or terphenyl-4-carboxylate ligands have been studied on the Au(111) and rutile TiO2(110) surfaces. We have used in situ electrospray deposition to produce a series of surface coverages from a fraction of a monolayer to multilayer films in both cases. X-ray absorption spectroscopy measured at the Mn L-edge (Mn 2p) has been used to study the effect of adsorption on the oxidation states of the manganese atoms in the core. In the case of the enzoate-functionalized complex, reduction of the manganese metal centres is observed due to the interaction of the manganese core with the underlying surface. In the case of terphenyl-4 carboxylate, the presence of this much larger ligand prevents the magnetic core from interacting with either the gold or the titanium dioxide surfaces and the characteristic Mn3+ and Mn4+ oxidation states necessary for magnetic behaviour are preserved. In contrast to the single molecule magnets where no charge transfer between the molecules and the substrates or within the molecules themselves were wanted, the molecules of bi isonicotinic acid and the giant zinc porphyrin nanorings have been studied on rutile TiO2(110) and Au(111) surfaces in the pursuit of charge transfer. In the case of the bi-isonicotinic acid it is studied on the rutile TiO2(110) where the technique of resonant inelastic X-ray scattering was been employed. Here we introduce the core-hole clock implementation to estimate the charge transfer from the molecule to the substrate. We verify previous results of ultrafast charge transfer in the sub-femtosecond regime (2.9 ± 0.3 femtoseconds) out of the LUMO+1 orbital. When the higher lying state of the LUMO+2 state is probed charge transfer out of this state and to the substrate is possibly there, but it is not possible to resolve it since it is masked by other effects originating from the inelastic scattering of the system. Furthermore, we see potential charge transfer within the molecule itself and new states observed in the inelastic scattering. Finally, zinc porphyrin nanorings were investigated on two surfaces of rutile TiO2(110) and Au(111). The techniques used here were X-ray photoemission spectroscopy and resonant photoemission spectroscopy. When the rutile TiO2(110) surface was employed hardly any participator decay was present suggesting charge transfer within the molecule itself or to the surface. This is further backed up by the fact that all of the core-excited unoccupied states are found to overlap energetically with the unoccupied states of the substrate, facilitating charge transfer out all the core-excited states. In the case of the Au(111) surface somewhat similar results are found, having all the core-excited states of the molecule located within the unoccupied states of the substrate, which again will facilitate charge transfer out all the core-excited states of the molecule. When the Au(111) substrate was employed the technique of near edge X-ray absorption fine structure was used to investigate the geometric orientation of the molecule on the surface. With the result of 86◦ ± 10◦ to the surface normal we verify previous scanning tunneling microscopy measurement that the zinc porphyrin nanorings will take a at lying orientation on the gold substrate.

This thesis investigates the dynamical properties of equilibrium and nonequilibrium systems, both quantum and classical, under the guise of a thermodynamic formalism. Large deviation functions associated with the generating functions of time-integrated observables play the role of dynamical free energies and thus determine the trajectory phase structure of a system. The 1d Glauber-Ising chain is studied using the time-integrated energy as the dynamical order parameter and a whole curve of second order trajectory transitions are uncovered in the complex counting field plane. The leading dynamical Lee-Yang zeros of the associated generating function are extracted directly from the time dependent high order cumulants. Resolving the cumulants into constituent contributions the motion of each contribution’s leading Lee-Yang zeros pair allows one to infer the positions of the trajectory transition points. Contrastingly if one uses the full cumulants only the positions of those closest to the origin, in the limit of low temperatures, can be inferred. Motivated by homodyne detection schemes this thermodynamic approach to trajectories is extended to the quadrature trajectories of light emitted from open quantum systems. Using this dynamical observable the trajectory phases of a simple “blinking” 3-level system, two weakly coupled 2-level systems and the micromaser are studied. The trajectory phases of this observable are found to either carry as much information as the photon emission trajectories or in some cases capture extra dynamically features of the system (the second example). Finally, the statistics of the time-integrated longitudinal and transverse magnetization in the 1d transverse field quantum Ising model are explored. In both cases no large deviation function exists but the generating functions are still calculable. From the singularities of these generating functions new transition lines emerge. These were shown to be linked to: (a) the survival probability of an associated open system, (b) PT-symmetry, (c) the temporal scaling of the cumulants and (d) the topology of an associated set of states.

Political deliberation is a classic component of collective decision-making. It consists in forming one’s political position through the give-and-take of reasons in the search of, but not necessarily reaching, consensus. Participants of genuine deliberation are open to transform their preferences in the light of persuasive arguments. Constitutional theory has borrowed this notion in its effort to reconstruct a justificatory discourse for judicial review of legislation. Constitutional courts were ascribed the pivotal role of implementing fundamental rights in most contemporary democracies and called for a more sophisticated picture of democratic politics. One influential defence has claimed that courts are not only insulated from electoral competition in order to guarantee the pre-conditions of majoritarian politics, but are deliberative forums of a distinctive kind: they are better located for public reasongiving. This belief has remained, from the normative point of view, largely underelaborated. The thesis proposes a model of deliberative performance to fill that gap. This qualitative concept unfolds the institutional and ethical requirements for courts to be genuinely deliberative. Instead of taking a stand on the old dispute about which institution is more legitimate to have the “last word” on constitutional meaning, this research leaves this question suspended and systematizes the large range of variations that can exist in constitutional courts’ performances. Discussions about the potential roles of constitutional courts, in this perspective, become more sensitive to contexts and to their varying degrees of legitimacy. The thesis offers a comprehensive picture of what is at stake if a constitutional court plans to be truly deliberative. This picture comprises the virtues presupposed by an ethics of deliberation, the institutional devices that facilitate deliberation, the approach to constitutional reasoning that is more hospitable to deliberation and, finally, the political perception to grasp the limits of deliberation itself.

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The adoption of the 2013 Constitution of Zimbabwe heralded a new era with high expectations from ordinary citizens of Zimbabwe. Among other matters, the Constitution provides for a multilevel system of government with government organised at the national, provincial and local levels. The design of this system of government is linked to the need, inter alia, to realise development, build democracy and sustain peace in Zimbabwe. Provincial and local governments are expected to play a role in the realisation of these goals. The question is whether the law and policy governing provincial and local governments in Zimbabwe enables these governments to play that role. It will be argued that the law and policy hinders the role of provincial and local governments in realising development, building democracy and sustaining peace. The national government has excessive supervisory powers over provincial and local governments which limit the minimum level of local discretion required if these lower governments are to assist in realising development, building democracy and sustaining peace. Moreover, the legal and institutional design emphasises coordinative rather than cooperative relations among governments, thereby undermining opportunities for effective multilevel governance. It will be argued that the 2013 Constitution, however, provides the foundation upon which an effective system of multilevel government can be built. Mere alignment of the legislative framework with the 2013 Constitution is nevertheless unlikely to give full effect to the non-centralised system of government envisaged by this new Constitution. What is required is the development of a policy, institutional and legislative framework that gives effect to the constitutional spirit of devolution of power and cooperative governance. / Doctor Legum - LLD

In this work we mainly focus on two main aspects of interest within the field of Relativistic Quantum Information. We first expand on the current knowledge of the effects of relativity on entanglement between global field modes. Within this aspect, we focus on two topics: we address and revise the single mode approximation commonly used in the literature. We study the nonlocal correlations of charged bosonic field modes and the degradation of entanglement initially present in maximally entangled states as a function of acceleration, when one observer is accelerated. In the second part of this work we introduce, develop and exploit a method for confining quantum fields within one (or two) cavities and analyzing the effects of motion of one cavity on the entanglement initially present between cavity field modes. One cavity is always allowed to undergo arbitrary trajectories composed of segments of inertial motion and uniform acceleration. We investigate how entanglement is degraded, conserved and created as a function of the parameters describing the motion and we provide the analytical tools to understand how these effects occur. We conclude this work by analyzing the effects of the change of spatial topology on the nonlocal correlations present in the Hawking-Unruh radiation in the topological geon analogue of black hole spacetimes.

We describe what can be called the “universal” phase space of 2+1 AdS gravity, in which the moduli spaces of globally hyperbolic AdS spacetimes with compact Cauchy surface, as well as the moduli spaces of multi black hole spacetimes are realized as submanifolds. Importantly our phase space also includes all Brown-Henneaux excitations on the conformal boundary of asymptotically AdS spacetimes, with Diff+(S1)/SL(2,R)xDiff+(S1)/SL(2,R) contained as a submanifold. Our description of the universal phase space is obtained from results on the correspondence between maximal surfaces in AdS3 and quasi-symmetric homeomorphisms of the unit circle. We find that the phase space can be parametrized by two copies of the universal Teichmuller space T(D), or equivalently by the cotangent bundle over T(D). This yields a symplectic map from T*T(D) to T(D)xT(D) generalizing the well-known Mess map in the compact spatial surface setting. We also relate our parametrization to the Chern-Simons formulation of 2+1 gravity and, infinitesimally, to the holographic (Fefferman-Graham) description. In particular, we relate the charges arising in the holographic description (such as the mass and angular momentum of asymptotically AdS spacetimes) to the periods of holomorphic quadratic differentials arising via the Bers embedding of T(D)xT(D).