Comment on ``Exact non-equilibrium transport through point contacts in quantum wires and fractional quantum Hall devices''

TL;DR

This paper critiques a previous derivation of non-equilibrium current in quantum Hall systems, highlighting a flaw in the use of equilibrium scattering matrices for finite bias conditions.

Contribution

It identifies a critical flaw in the derivation of non-equilibrium current, emphasizing the need for careful treatment beyond linear response.

Findings

The original result is valid only in the linear response limit.

Using equilibrium scattering matrices out of equilibrium is unjustified.

The derivation should be revisited for finite bias conditions.

Abstract

Fendley, Ludwig and Saleur [Phys. Rev. B52 (1995) 8934] have obtained an expression for the non-equilibrium current through a constriction in the quantum Hall bar based on the Bethe ansatz technique and the Bolzmann equation. In this Comment we draw attention to a serious flaw in their derivation. We argue that their result is correct in the linear response limit but should be taken with a care out of equilibrium for finite bias. The reason is in the use of the equilibrium scattering matrix in the place of the transition probability amplitude out of equilibrium, the substitution which was not shown to be legimate.