  We study a system consisting of a Luttinger liquid coupled to a quantum dot
on the boundary. The Luttinger liquid is expressed in terms of fermions
interacting via density-density coupling and the dot is modeled as an
interacting resonant level on to which the bulk fermions can tunnel. We solve
the Hamiltonian exactly and construct all eigenstates. We study both the zero
and finite temperature properties of the system, in particular we compute the
exact dot occupation as a function of the dot energy in all parameter regimes.
The system is seen to flow from weak to to strong coupling for all values of
the bulk interaction, with the flow characterized by a non-perturbative Kondo
scale. We identify the critical exponents at the weak and strong coupling
regimes.
