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 $I\sim \exp(-E_0/eV)$, where $E_0\sim\eta/\kappa$ and $\kappa$ denotes the compressibility and $\eta$ the dissipation strength. At nonzero temperature $T$, the linear conductance is proportional to $\exp(-\sqrt{{\mathcal{C}}E_0/k_B T})$. The decay of Friedel oscillation saturates for at distances larger than $L_{\eta}\sim 1/\eta$ from the impurity.\newline [1] Z. Ristivojevic and T. Nattermann, Phys. Rev. Lett. \textbf{101}, 016405 (2008).