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

Eldad Bettelheim·Alexander G. Abanov·Paul Wiegmann
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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.

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Eldad Bettelheim, Alexander G. Abanov, Paul Wiegmann. 2006-06-29. Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids. https://doi.org/10.1103/physrevlett.97.246401

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