Research

Publications on Google Scholar.

A rigorous approach to quantum integrable models at finite temperature  (2019, Ph.D Thesis)

Abstract: This thesis develops a rigorous framework allowing one to prove the exact representations for various observables in the XXZ Heisenberg spin-1/2 chain at finite temperature. Previously it has been argued in the literature that the per-site free energy or the correlation lengths admit integral representations whose integrands are ex- pressed in terms of solutions of non-linear integral equations. The derivations of such representations relied on various conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the exchangeability of the infinite volume limit and the Trotter number limits, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations and finally the identification of the quantum transfer matrix’ s Eigenvalues with solutions to the non-linear integral equation. We rigorously prove all these conjectures in the high temperature regime. Our analysis also allows us to prove that for temperatures high enough, one may describe a certain subset of sub-dominant Eigenvalues of the quantum transfer matrix described in terms of solutions to a spin-1 chain of finite length.

Conformal field theory and two dimensional critical phenomena (2016, Master’s Thesis)

Abstract: We explore the representations of the underlying infinite dimensional symmetry algebra in two dimensional quantum field theory. This provides a window to study the algebra of local fields which is central to the description of two dimensional critical phenomena that emerges in the scaling limit of certain statistical systems on a two-dimensional lattice. Unitary minimal models are then constructed from such representations and the first few series of the set of minimal theories are shown to correspond to some well-known statistical systems. The systems studied in particular are the Ising and the tricritical Ising models. Potential interactions between Ising fermions and bosons in two dimensions occurring within the framework of specific condensed matter models at criticality are reviewed using arguments from conformal invariance.

Dynamics of an Inflationary Universe (2015, Undergraduate Thesis )

Abstract: The initial conditions needed by the standard cosmological model lead to precarious features. This motivates the search for a completely new picture of the early universe which is the inflationary scenario. Contained within this report is a study of the standard cosmological model followed by the development of the paradigm of inflation within the context of chaotic and standard model Higgs inflation. The phenomenon of reheating is examined as a two stage process; preheating and thermalisation. Normalisation of the inflationary models according to data from the cosmic microwave background anisotropy is discussed. The theoretical predictions and experimental values of the cosmological parameters are then compared.