Fermi Edge Resonances in Non-equilibrium States of Fermi Gases

TL;DR

This paper develops a mathematical framework to analyze Fermi Edge Singularity in non-equilibrium Fermi gases, revealing integrable structures and extending bosonic methods to non-equilibrium conditions.

Contribution

It formulates the problem as a matrix Riemann-Hilbert problem and extends bosonic approaches to non-equilibrium Fermi states.

Findings

Formulation as a matrix Riemann-Hilbert problem for non-equilibrium states

Reveals integrable structure of the Fermi Edge Singularity

Provides a method to extract leading asymptotes in non-equilibrium conditions

Abstract

We formulate the problem of the Fermi Edge Singularity in non-equilibrium states of a Fermi gas as a matrix Riemann-Hilbert problem with an integrable kernel. This formulation is the most suitable for studying the singular behavior at each edge of non-equilibrium Fermi states by means of the method of steepest descent, and also reveals the integrable structure of the problem. We supplement this result by extending the familiar approach to the problem of the Fermi Edge Singularity via the bosonic representation of the electronic operators to non-equilibrium settings. It provides a compact way to extract the leading asymptotes.