Quantum shockwave at the quasi-relativistic resonance

Abstract

Shockwaves are violent nonlinear distortions of wave motion which have been reported in fluid waves and electromagnetic waves, while here we reveal that a shockwave can occur even in the quantum wave function of a single particle. Specifically, we analyze the electromagnetic field travelling on resonance with the limiting velocity of the quasi-relativistic particle, and reveal that a strong longitudinal field can rip up a quantum shockwave singularity in the particle wave function, leading to energy dissipation. Moreover, we show that this effect is particularly strong for quasi-relativistic (Dirac) electrons in graphene for two reasons. On one hand, we obtain the single-particle shockwave at very small fields due to the small effective electron mass, and on the other hand we can obtain large dissipation in the many-particle shockwave by using the large electron density in graphene. While the single-particle shockwave can be most easily observed by locating the shockwave singularity with a high-resolution microscopy, the many-particle dissipation would be simply observed as a rapid decay of our resonant electromagnetic field.