Energy and particle currents in a driven integrable system

TL;DR

This paper investigates the ratio of energy to particle currents in a driven one-dimensional integrable fermion system, revealing conditions where the ratio aligns or diverges from linear-response predictions.

Contribution

It demonstrates how the energy-to-particle current ratio behaves in different regimes of an integrable system under a dc electric field, highlighting deviations from linear-response theory.

Findings

In doped insulators, the ratio matches linear-response predictions.

In metallic regimes, the ratio exceeds linear-response estimates.

The ratio's behavior depends on the saturation of the Mazur bound.

Abstract

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.