  We present methods of finding complex eigenvalues of the Liouvillian of an
open quantum system. The goal is to find eigenvalues that cannot be predicted
from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type
quantum dot with an infinitely long lead. We suggest the existence of the
non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that
the original problem reduces to the problem of a two-particle Hamiltonian with
a two-body interaction and the other way is to show that diagram expansion of
the Green's function has correlation between the bra state and the ket state.
We also introduce the integral equations equivalent to the original eigenvalue
problem.
