Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
Strongly Correlated Electrons
2007-05-23 v1 Mesoscale and Nanoscale Physics
High Energy Physics - Theory
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.cond-mat/0606778,
title = {Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids},
author = {Eldad Bettelheim and Alexander G. Abanov and Paul Wiegmann},
journal= {arXiv preprint arXiv:cond-mat/0606778},
year = {2007}
}