Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids

TL;DR

This paper demonstrates that non-linear effects, arising from spectrum curvature, lead to shock wave phenomena and soliton trains with fractional charge in electronic liquids, with implications for observing quantum shock waves.

Contribution

It introduces the concept of quantum shock waves in electronic liquids using the Calogero model, highlighting non-linear effects and fractional charge solitons.

Findings

Non-linear transport due to spectrum curvature.

Formation of shock wave singularities and oscillatory structures.

Emergence of fractional charge soliton trains.

Abstract

Using the Calogero model as an example, we show that the transport in interacting non-dissipative electronic systems is essentially non-linear. Non-linear effects are due to the curvature of the electronic spectrum near the Fermi energy. As is typical for non-linear systems, propagating wave packets are unstable. At finite time shock wave singularities develop, the wave packet collapses, and oscillatory features arise. They evolve into regularly structured localized pulses carrying a fractionally quantized charge - {\it soliton trains}. We briefly discuss perspectives of observation of Quantum Shock Waves in edge states of Fractional Quantum Hall Effect and a direct measurement of the fractional charge.