  We study the effects of electron-phonon interactions on the transport
properties of a molecular quantum dot coupled to two Luttinger-liquid leads. In
particular, we investigate the effects on the steady state current and DC noise
characteristics. We consider both equilibrated and unequilibrated on-dot
phonons. The density matrix formalism is applied in the high temperature
approximation and the resulting semi-classical rate equation is numerically
solved for various strengths of electron-electron interactions in the leads and
electron-phonon coupling. The current and the noise are in general smeared out
and suppressed due to intralead electron interaction. On the other hand, the
Fano factor, which measures the noise normalized by the current, is more
enhanced as the intralead interaction becomes stronger. As the electron-phonon
coupling becomes greater than order one, the Fano factor exhibits
super-Poissonian behaviour.
