Studies in quantum field theory at finite temperature

The thesis deals with certain quantum field systems exhibiting spontaneous symmetry breaking and their response to temperature. These models find application in diverse branches such as particle physics, solid state physics and non~linear optics. The nature of phase transition that these systems may undergo is also investigated. The thesis contains seven chapters. The first chapter is introductory and gives a brief account of the various phenomena associated with spontaneous symmetry breaking. The chapter closes with anote on the effect of temperature on quantum field systems. In chapter 2, the spontaneous symmetry breaking phenomena are reviewed in more detail. Chapter 3, deals with the formulation of ordinary and generalised sine-Gordon field theories on a lattice and the study of the nature of phase transition occurring in these systems. In chapter 4, the effect of temperature on these models is studied, using the effective potential method. Chapter 5 is a continuation of this study for another model, viz, the m6 model. The nature of phase transition is also studied. Chapters 5 and 6 constitute a report of the investigations on the behaviour of coupling constants under thermal excitation D1 $4 theory, scalar electrodynamics, abelian and non-abelian gauge theories

Scaling relations in the Lyapunov exponents of one dimensional maps

We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map. where the scaling index is found to be different.

Studies on gaussian effective potentials in some models

In classical field theory, the ordinary potential V is an energy density for that state in which the field assumes the value ¢. In quantum field theory, the effective potential is the expectation value of the energy density for which the expectation value of the field is ¢o. As a result, if V has several local minima, it is only the absolute minimum that corresponds to the true ground state of the theory. Perturbation theory remains to this day the main analytical tool in the study of Quantum Field Theory. However, since perturbation theory is unable to uncover the whole rich structure of Quantum Field Theory, it is desirable to have some method which, on one hand, must go beyond both perturbation theory and classical approximation in the points where these fail, and at that time, be sufficiently simple that analytical calculations could be performed in its framework During the last decade a nonperturbative variational method called Gaussian effective potential, has been discussed widely together with several applications. This concept was described as a means of formalizing our intuitive understanding of zero-point fluctuation effects in quantum mechanics in a way that carries over directly to field theory.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Thermohaline variability in the upper layers of the Arabian Sea

The Arabian Sea is an area of complex air-sea interaction processes with seasonal reversing monsoons. The associated thermohaline variability in the upper layers appears to control the large scale monsoon flow which is not yet completely understood. The variability in the thermohaline fields is known to occur in temporal domain ranging from intra-diurnal to inter-annual time scales and on spatial domains of few tens of kilometers to few thousands of kilometers. In the Arabian Sea though the surface temperature was routinely measured by both conventional measurements and satellites, the corresponding information on the subsurface thermohaline field is very sparse due to the lack cw adequate measurements. In such cases the numerical models offer promise in providing information on the subsurface features given an initial thermohaline field and surface heat flux boundary conditions. This thesis is an outcome of investigations carried out on the various aspects of the thermohaline variability on different time scales. In addition to the description of the mean annual cycle. the one dimensional numerical models of Miller (1976) and Price et a1 (1986) are utilised to simulate the observed mixed layer characteristics at selected locations in the Arabian Sea on time scales ranging from intra-diurnal to synoptic scales under variable atmospheric forcing.

Synthesis of High Coercivity Cobalt Nanotubes with Acetate Precursors and Elucidation of the Mechanism of Growth

Cobalt nanotubes (CoNTs) with very high longitudinal coercivity were prepared by electrodeposition of cobalt acetate for the first time by using anodized alumina (AAO) template. They were then characterized with X-ray diffraction (XRD), a field emission scanning electron microscope (FESEM), and a transmission electron microscope (TEM). Formation of a highly ordered hexagonal cobalt phase is observed. Room temperature SQUID (superconducting quantum interference device) magnetometer measurements indicate that the easy axis of magnetization is parallel to the nanotube axis. These CoNTs exhibit very high longitudinal coercivity of ∼820 Oe. A very high intertubular interaction resulting from magnetostatic dipolar interaction between nanotubes is observed. Thick-walled nanotubes were also fabricated by using cobalt acetate tetrahydrate precursors. A plausible mechanism for the formation of CoNTs based on mobility assisted growth is proposed. The role of the hydration layer and the mobility of metal ions are elucidated in the case of the growth mechanism of one-dimensional geometry

The synthesis of high coercivity cobalt-in-carbon nanotube hybrid structures and their optical limiting properties

Magnetic heterostructures with carbon nanotubes having multiple functionalities are fascinating materials which can be manipulated by means of an external magnetic field. In this paper we report our investigations on the synthesis and optical limiting properties of pristine cobalt nanotubes and high coercivity cobalt-in-carbon nanotubes (a new nanosystem where carbon nanotubes are filled with cobalt nanotubes). A general mobility assisted growth mechanism for the formation of one-dimensional nanostructures inside nanopores is verified in the case of carbon nanotubes. The open-aperture z-scan technique is employed for the optical limiting measurements in which nanosecond laser pulses at 532 nm have been used for optical excitation. Compared to the benchmark pristine carbon nanotubes these materials show an enhanced nonlinear optical absorption, and the nonlinear optical parameters calculated from the data show that these materials are efficient optical limiters. To the best of our knowledge this is the first report where the optical limiting properties of metal nanotubes are compared to those of carbon nanotubes