  In this work, the correlation functions of a Luttinger liquid with a cluster
of impurities around an origin obtained using the Non chiral bosonization
technique (NCBT) are used to study two important physical phenomena, viz.,
conductance and resonant tunneling. The latter is studied when the cluster
consists of two impurities separated by a distance (measured in units of the
Fermi wavelength). Conductance is studied both in the Kubo formalism, which
relates it to current-current correlations (four-point functions), as well as
the outcome of a tunneling phenomena (two-point functions). In both the cases,
closed analytical expressions for conductance are calculated and a number of
interesting physical observations are discussed, besides presenting a favorable
comparison with the existing literature.
