Quantum shockwave at the quasi-relativistic resonance

We analyze the electromagnetic field travelling on resonance with the limiting velocity of the quasi-relativistic particle. We show that a strong longitudinal field leads to the quantum wave function singularity in the form of a shockwave, accompanied by strong energy dissipation. We show that the effect is particularly strong in the case of Dirac electrons in graphene due to the small effective mass. We discuss several experimental tests of these predictions.