In this thesis we present theoretical analysis for three problems in condensed matter physics. We present theoretical study of quantum phase transition from one-dimension to a quasi-one-dimensional state in interacting quantum wires, a proposal for realization of one-
way waveguides and the calculation of magentoelectric coefficients for composite magnetoelectrics.
In part I of the thesis we present a theoretical study of the quantum phase transition from one-dimension to a quasi-one-dimensional state in interacting quantum wires. We analytically study the quantum phase transition at strong and weak coupling and identify the nature of the transition of the quantum phase transition in these limits. At strong interactions we find that the spin sector is completely decoupled from the charge sector and
identify the transition to be an Ising transition. At weak interactions we find the transition to be a Lifshitz transition of strongly interacting polarons.
In part II of the thesis we present a theoretical proposal for realization of one-way waveguides. We then discuss theoretical calculations for band-structure of photonic crystals with magnetically anisotropic components.
In part III of the thesis we present calculations for the effective magnetoelectric coefficients of a composite magnetoelectric.