Energy and particle currents in a driven integrable system

We study the ratio of the energy and particle currents ($j^E/j^N$) in an integrable one dimensional system of interacting fermions. Both currents are driven by a finite (nonzero) dc electric field. In doped insulators, where the local conserved quantities saturate the so called Mazur bound on the charge stiffness, $j^E/j^N$ agrees with the linear--response theory, even though such agreement may be violated for each current alone. However, in the metallic regime with a non-saturated Mazur bound, the ratio $j^E/j^N$ in a driven system is shown to be much larger than predicted by the linear--response theory.