Quantum ripples over a semi-classical shock

TL;DR

This paper investigates how quantum effects induce ripples in shock waves within a one-dimensional Fermi gas, revealing that these ripples are determined by classical density profiles despite their quantum nature.

Contribution

It demonstrates that quantum corrections produce density ripples over classical shock waves, with ripple characteristics derived solely from classical density profiles.

Findings

Quantum ripples appear at shock wave kinks.

Ripple amplitude and period depend only on classical density profiles.

Quantum effects modify classical shock wave evolution.

Abstract

The evolution of an initially smooth spatial inhomogeneity in the density of a one-dimensional Fermi gas is well described by classical mechanics. The classical evolution leads to the formation of a shock wave: the density develops kinks in its coordinate dependence. We show that quantum corrections to the shock wave produce density ripples which run off the kinks. Despite their quantum origin, the amplitude and period of the ripples are expressed only in terms of classical objects derived from a smooth density profile.