Transport in a dissipative luttinger liquid

We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (Ohmic) bath. For nonzero dissipation, the single impurity is always a relevant perturbation which suppresses transport strongly. At zero temperature, the current voltage relation of the link is I similar to exp(-E(0)/eV), where E(0)similar to eta/kappa and kappa denotes the compressibility. At nonzero temperature T, the linear conductance is proportional to exp(-root CE(0)/k(B)T). The decay of Friedel oscillation saturates for a distance larger than L(eta)similar to 1/eta from the impurity.