Conductance of a fully equilibrated quantum wire

We study electronic transport properties of a long weakly interacting homogeneous quantum wire, connected to non-interacting leads. From Galilean invariance of the system we infer that in a state with a finite electric current, the electrons reach thermal equilibrium in a frame moving with their drift velocity. At non-zero temperature the resulting distribution function inside the wire is slightly different from the distribution supplied by the leads. This gives rise to a small correction to the quantized value of conductance $2e^2/h$, which can be found by performing a careful analysis of the conservation laws. The correction is of the order of $\left(T/E_F\right)^2$ and does not depend on the details of the electron-electron interaction.