Excess energy and countercurrents after a quantum kick

A system of interacting quantum particles under a static potential is "kicked" when the potential suddenly starts moving at a constant velocity, v. For a stationary initial state, the excess energy at any time after the kick is v · ⟨P⟩(t), where P is the system’s total momentum. In finite bound systems, the long-time average excess energy approaches Mv², which is twice the value for a smooth onset of motion. Macroscopic systems develop a counterflow of particles that opposes the moving potential. This is formally analogous to an infinitely short electric-field pulse for charged particles, where E = mvδ(t)/q. In metals, linear response theory shows that the Drude weight determines the low-v countercurrent. In contrast, insulators exhibit non-linear countercurrents due to electron-hole excitations induced by the kick. First-principles calculations for simple solids support these predictions, which should also apply to systems such as Mott insulators and cold atom lattices.