The threshold effects in one-dimensional strongly-interacting systems out of equilibrium

TL;DR

This paper develops a perturbation theory to analyze threshold phenomena in strongly interacting one-dimensional systems out of equilibrium, extending previous results to systems lacking free-fermionic excitations.

Contribution

It introduces a novel perturbative approach that applies to a broader class of strongly interacting systems, including fractional quantum Hall edges.

Findings

Reproduces known results for quantum Hall edge relaxation.

Extends analysis to systems without free-electron excitations.

Provides asymptotic behavior near excitation thresholds.

Abstract

In this work we investigate the phenomena associated with the new thresholds in the spectrum of excitations arising when different one-dimensional strongly interacting systems are voltage biased and weakly coupled by tunneling. We develop the perturbation theory with respect to tunneling and derive an asymptotic behavior of physical quantities close to threshold energies. We reproduce earlier results for the electron relaxation at the edge of an integer quantum Hall system and for the non-equilibrium Fermi edge singularity phenomenon. In contrast to the previous works, our analysis does not rely on the free-fermionic character of local tunneling, therefore we are able to extend our theory to wider class of systems, without well-defined electron excitations, such as spinless Luttinger liquids and chiral quantum Hall edge states at fractional filling factors.