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Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas

E. Bettelheim·A. G. Abanov·P. Wiegmann
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Abstract

A semiclassical wave-packet propagating in a dissipationless Fermi gas inevitably enters a "gradient catastrophe" regime, where an initially smooth front develops large gradients and undergoes a dramatic shock wave phenomenon. The non-linear effects in electronic transport are due to the curvature of the electronic spectrum at the Fermi surface. They can be probed by a sudden switching of a local potential. In equilibrium, this process produces a large number of particle-hole pairs, a phenomenon closely related to the Orthogonality Catastrophe. We study a generalization of this phenomenon to the non-equilibrium regime and show how the Orthogonality Catastrophe cures the Gradient Catastrophe, providing a dispersive regularization mechanism. We show that a wave packet overturns and collapses into modulated oscillations with the wave vector determined by the height of the initial wave. The oscillations occupy a growing region extending forward with velocity proportional to the initial height of the packet. We derive a fundamental equation for the transition rates (MKP-equation) and solve it by means of the Whitham modulation theory.

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E. Bettelheim, A. G. Abanov, P. Wiegmann. 2006-08-21. Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas. https://doi.org/10.1103/physrevlett.97.246402

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