Transport in a Dissipative Luttinger Liquid

Abstract

We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (ohmic) bath . For non-zero dissipation $η$ the weak link 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 $E_0\simη/κ$ and $κ$ denotes the compressibility. At non-zero temperature $T$ the linear conductance is proportional to $\exp(-\sqrt{{\cal C}E_0/k_BT})$. The decay of Friedel oscillation saturates for distance larger than $L_η\sim 1/η$ from the impurity.

4 pages