  A multiply connected system in both its open and closed form variations but
in equilibrium is studied using quantum waveguide theory. The system exhibits
remarkable features, in its open form variation we see current enhancement,
hitherto seen only in non-equilibrium systems in absence of magnetic flux. In
its closed form analog parity effects are broken. Further we analyse the global
and local current densities of our system and also show that the orbital
magnetic response of the system calculated from the current densities (and
inherently linked to the topological configuration) is qualitatively not same
as that calculated from the eigenenergy spectra.
