In this thesis we shall be concerned with the study of models which arise as a consequence of adopting discrete regularisations for various Euclidean space quantum field theories. Specifically, we employ a random triangulation of the continuum space, and define the fields only over nodes or links of the mesh. Lattice field theories, together with the Renormalisation Group, are introduced in the first chapter. Continuum physics is shown to depend on the positions and stabilities of zeroes of the β-function, which in turn requires a knowledge of the critical behaviour of the associated statistical model. In Chapter 2. we examine a theory of Dirac fermions in 2 + 1 dimensions on a random lattice. We investigate the behaviour of the 2-pt function and fermion condensate in the absence of any background gauge field. The results indicate certain doubling problems, generic to regular lattice formulations of fermion field theories, are evaded, at least at tree graph level. We then go on to examine the fermion vacuum currents in the presence of background fields with non-zero winding number. We are able to demonstrate the existence of a Chern-Simon's topological term in the gauge field effective action which yields parity violating vacuum currents. The magnitude of these are in agreement with certain continuum calculations. The final chapter concerns the properties of random surfaces. The particular class of models chosen originate as discretisations of Polyakov's string. The partition function is approximated by a sum over all possible random triangulations and an integral over vertex positions. The sum over random lattices is intended to mimick the functional integral over intrinsic metrics encountered in the continuum, and the model may also be pictured as 2D quantum gravity coupled to a scalar field. We consider the phase structure of the models when two forms of extrinsic curvature are added to the standard action. Monte-Carlo simulation indicates that with one type of curvature term a strong 2^nd order phase transition exists at finite coupling, leading to a new continuum limit for the model possessing long-range correlation properties. With the other type a much weaker higher order transition is observed. In this case the surface will be crumpled at long distance. We discuss the implications of these results for continuum surfaces.

Thesis (M.S. in Physics)--United States Naval Postgraduate School, California. / Includes bibliographical references (p. 23). 9

The linearized Einstein equation describing graviton propagation through a chiral medium appears to be helicity dependent. We analyze features of the corresponding spectrum in a collision-less regime above a flat background. In the long wave-length limit, circularly polarized metric perturbations travel with a helicity dependent group velocity that can turn negative giving rise to a new type of an anomalous dispersion. We further show that this chiral anomalous dispersion is a general feature of polarized modes propagating through chiral plasmas extending our result to the electromagnetic sector.

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Near-field thermophotovoltaic (NFTPV) devices have received great attention lately as attractive energy harvesting systems, whereby a heated thermal emitter exchanges super-Planckian near-field radiation with a photovoltaic (PV) cell to generate electricity. This work describes the advancement of NFTPV technology through both simulations of next-generation devices, and experimental research addressing the technical challenges faced by NFTVPs, including nanostructured material properties, and large-area near-field heat transfer. The first part of this work seeks to improve the performance of a possible NFTPV device by using a periodic tungsten grating as the thermal emission source. The effects on the electrical power generation and the conversion efficiency are investigated via simulations with different grating geometries. It is found that using the selected grating geometry the power output and efficiency could be increased by 40% and 6%, respectively, over a flat tungsten emitter. The reasoning behind the enhancement is attributed to a plasmonic resonance that shifts towards lower frequencies at large wavenumbers. Extensive experimental research is undertaken to investigate the technical challenges in NFTPVs. The optical properties of thin tungsten films, which may serve as an emitter material, are extracted through spectroscopic measurements, and are found to be significantly different from reported bulk values due to a wide range of crystal structures that are present in sputtered films. A heat transfer experiment is designed and built to measure near-field radiation between two doped-silicon slabs separated by a submicron vacuum gap. The details of this system and the sample fabrication show a robust and straightforward method of measuring large-area near-field radiative heat transfer at distances between 200 nm and 800 nm. The results of this experiment show the largest energy throughput of submicron near-field heat transfer to date, and serve to address technical challenges behind practical near-field thermophotovoltaic technology.

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published_or_final_version / Physics / Master / Master of Philosophy

When any method of surface wave testing that involves Rayleigh waves is performed, one important assumption is that plane Rayleigh waves are being measured. In the forward modeling or inversion procedure that is used to analyze the field dispersion curve to determine the field V[subscript s] profile, the analysis is based on the wave field consisting of plane Rayleigh waves. Therefore, field dispersion curves that contain near-field data could adversely distort the field V[subscript s] profile. To minimize the influence of near-field effects, several criteria have been recommended in the past. However, most of the criteria were based on empirical equations that implicitly assumed zones of influence, or numerical simulations. There is a lack of experimental investigation, particularly full-scale field investigations. Even, the numerical solutions have been based on simple soil profiles without significant velocity contrasts between soil layers and/or varying thicknesses of soil layers which can significantly influence near-field effects. Data from full-scale field test using the Spectral-Analysis-of-Surface-Waves (SASW) method was used in this thesis research. SASW tests performed at two stages in the construction of a deep, 90-ft thick backfill were studied. The V[subscript s] profiles were normally dispersive, with a substantial increase in the velocity of the layer beneath the backfill. The study shows the adverse distortions that can occur in the field dispersion curve from near-field effects when the spacing of the receiver pair is: (1) above the zone of rapidly increasing V[subscript s] near the surface and (2) less than the depth to the stiffer layer in deeper measurements. Other factors that affect the results are discussed and recommendations are presented to minimize the introduction of near-field effects, at least in these relatively simple V[subscript s] profiles. / text