Gradient Catastrophe and Fermi Edge Resonances in Fermi Gas

TL;DR

This paper investigates how a smooth disturbance in a Fermi gas leads to a gradient catastrophe, causing the Fermi surface to become sharp and resulting in multiple asymmetric singularities in Fermi edge measurements.

Contribution

It introduces a mathematical framework for analyzing Fermi edge singularities using a matrix Riemann-Hilbert problem and explores the effects of gradient catastrophe on spectral features.

Findings

Gradient catastrophe causes multiple asymmetric Fermi edge resonances.

Single-peaked Fermi-edge singularity transforms into multiple peaks.

Mathematical formulation via Riemann-Hilbert problem enhances understanding.

Abstract

A smooth spatial disturbance of the Fermi surface in a Fermi gas inevitably becomes sharp. This phenomenon, called {\it the gradient catastrophe}, causes the breakdown of a Fermi sea to disconnected parts with multiple Fermi points. We study how the gradient catastrophe effects probing the Fermi system via a Fermi edge singularity measurement. We show that the gradient catastrophe transforms the single-peaked Fermi-edge singularity of the tunneling (or absorption) spectrum to a set of multiple asymmetric singular resonances. Also we gave a mathematical formulation of FES as a matrix Riemann-Hilbert problem.