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

摘要

Using the Calogero model as an example, we show that the transport ininteracting non-dissipative electronic systems is essentially non-linear.Non-linear effects are due to the curvature of the electronic spectrum near theFermi energy. As is typical for non-linear systems, propagating wave packetsare unstable. At finite time shock wave singularities develop, the wave packetcollapses, and oscillatory features arise. They evolve into regularlystructured localized pulses carrying a fractionally quantized charge - {\itsoliton trains}. We briefly discuss perspectives of observation of QuantumShock Waves in edge states of Fractional Quantum Hall Effect and a directmeasurement of the fractional charge.