Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas

TL;DR

This paper explores how the Orthogonality Catastrophe regularizes shock wave formation in a non-equilibrium Fermi gas, revealing dispersive effects and wave modulation phenomena through theoretical analysis.

Contribution

It introduces a generalized Orthogonality Catastrophe mechanism that prevents gradient catastrophes in non-equilibrium Fermi gases, using the MKP-equation and Whitham theory.

Findings

Orthogonality Catastrophe cures gradient catastrophe in non-equilibrium Fermi gases.

Wave packets develop modulated oscillations with velocity proportional to initial height.

Derived and solved the MKP-equation for transition rates.

Abstract

A semiclassical wave-packet propagating in a dissipationless Fermi gas inevitably enters a "gradient catastrophe" regime, where an initially smooth front develops large gradients and undergoes a dramatic shock wave phenomenon. The non-linear effects in electronic transport are due to the curvature of the electronic spectrum at the Fermi surface. They can be probed by a sudden switching of a local potential. In equilibrium, this process produces a large number of particle-hole pairs, a phenomenon closely related to the Orthogonality Catastrophe. We study a generalization of this phenomenon to the non-equilibrium regime and show how the Orthogonality Catastrophe cures the Gradient Catastrophe, providing a dispersive regularization mechanism. We show that a wave packet overturns and collapses into modulated oscillations with the wave vector determined by the height of the initial wave. The oscillations occupy a growing region extending forward with velocity proportional to the initial height of the packet. We derive a fundamental equation for the transition rates (MKP-equation) and solve it by means of the Whitham modulation theory.