Das, Joy Prakash2020-06-302023-10-262020-06-302023-10-262019ROLL NO.146121021https://gyan.iitg.ac.in/handle/123456789/1434Supervisor: Girish S. SetlurIn this work, the powerful Non-chiral bosonization technique (NCBT) is introduced, which is a non-trivial modification of the standard Fermi-Bose correspondence in one spatial dimension made in order to facilitate the study of strongly inhomogeneous Luttinger liquids (LL) where the properties of free fermions plus the source of inhomogeneities are reproduced exactly. The formalism is applied to obtain the correlation functions of translationally non-invariant systems like LL with a cluster of impurities (barriers/wells) around an origin, a one step fermionic ladder, slowly moving impurities in a Luttinger liquid, etc. The obtained correlation functions are used to study various physical phenomena like Friedel oscillations, resonant tunneling, dynamical density of states, conductance, mobility (in case of mobile impurities) and so on. The results are validated using the Schwinger Dyson equation and perturbative methods. The present method is superior to the conventional bosonization methods (g-ology methods) which requires additional tools like re-normalization, etc. to deal with impurities.enPHYSICSThesis