Excess energy and countercurrents after a quantum kick

A quantum system of interacting particles under the effect of a static external potential is hereby described as kicked when that potential suddenly starts moving with a constant velocity v. If initially in a stationary state, the excess energy at any time after the kick equals $v \langle P \rangle (t)$, with P being the total momentum of the system. If the system is finite and remains bound, the long time average of the excess energy tends to $Mv^2$, with M the system's total mass, or a related expression if there is particle emission. $Mv^2$ is twice what expected from an infinitely smooth onset of motion, and any monotonic onset is expected to increase the average energy to a value within both limits. In a macroscopic system, a particle flow emerges countering the potential's motion when electrons stay partially behind. For charged particles the described kinetic kick is equivalent to the kick given by the infinitely short electric-field pulse $E = \frac{m}{q} v \delta (t)$ to the system at rest, useful as a formal limit in ultrafast phenomena. A linear-response analysis of low-v countercurrents in kicked metals shows that the coefficient of the linear term in v is the Drude weight. Non-linear in v countercurrents are expected for insulators through the electron-hole excitations induced by the kick, going as $v^3$ at low v for centrosymmetric ones. First-principles calculations for simple solids are used to ratify those predictions, although the findings apply more generally to systems such as Mott insulators or cold lattices of bosons or fermions.