  We study the nonequlibrium transport through a quantum dot weakly coupled to
Luttinger liquids (LL). A general current expression is derived by using
nonequilibrium Green function method. Then a special case of the dot with only
a single energy level is discussed. As a function of the dot's energy level, we
find that the current as well as differential conductance is strongly
renormalized by the interaction in the LL leads. In comparison with the system
with Fermi liquid (FL) leads, the current is suppressed, consistent with the
suppression of the electron tunneling density of states of the LL; and the
outset of the resonant tunneling is shifted to higher bias voltages. Besides,
the linear conductance obtained by Furusaki using master equation can be
reproduced from our result.
