Orthogonality Catastrophe and Shock Waves in a Nonequilibrium Fermi Gas

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 nonlinear 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 nonequilibrium regime and show how the orthogonality catastrophe cures the gradient catastrophe, by providing a dispersive regularization mechanism.

Figure 1

(a) A shock-wave solution of the Riemann Eq. (9). The vertical lines are trailing and leading edges. The solid arrows show the relations between branches of the multivalued solution of the Riemann equation and Whitham modulated particle $P$, hole $Q$ and Fermi $P_F$ momenta. (b) Oscillations obtained by the Whitham method, the dashed red line shows the unphysical part of the Riemann solution.