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.

The assignment and analysis of high resolution spectra of transient species in the gas phase leads to the unambiguous identification of the carrier of the spectra. Such spectra can only be observed provided a detectable steady state concentration, depending on the particular spectroscopic technique being employed, can be generated. The first half of this thesis is concerned with three methods of producing detectable concentrations by utilising (i) microwave discharge, (ii) electrical discharge, (iii) carbon dioxide laser photolysis with an associated photosensitiser, sulphur hexafluoride. The high resolution electron paramagnetic resonance spectra of iodine and fluorine atoms and the sulphur monoxide and nitrogen difluoride radicals serve as examples of species produced by these methods and some characteristics of the laser photolysis technique are described in Chapter IV. The advent of the infrared semiconductor diode laser and also a solid state millimeter wave source (an IMPATT oscillator, in conjunction with the technique of magnetic resonance) has led to the development of more sensitive high resolution spectroscopic techniques. High resolution spectra of the important silicon monohydride radical have been observed using the former technique and the experiments and subsequent analysis are described in Chapter VI. The millimeter wave magnetic resonance spectrometer designed and constructed by the author is described in Chapter VII, together with the millimeter wave magnetic resonance spectrum of the oxygen molecule, the first spectrum to be observed by this new technique.

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