The Quantum Boomerang Effect

Dominique Delande
Laboratoire Kastler-Brossel, Case 74, Sorbonne Université, 4 place Jussieu 75005 Paris

When a wavepacket is launched with a finite velocity in free space, it follows a balistic motion, both in classical and quantum mechanics. In the presence of a disordered potential, the generic classical behavior, described by the Boltzman equation, is a random walk - that is a diffusive motion at long time - whose charateristic length is the mean free path. The center of mass of the classical "wavepacket" first drifts balistically in the direction of the initial velocity, slowly slows down and ends up at long time displaced by one mean free path. The quantum dynamics is drastically different: the center of mass first drifts balistically, but rapidly performs a U-turn and slowly returns to its initial position. I will describe this "Quantum Boomerang" effect both numerically and analytically in dimension 1, and show that it is partially destroyed by weak particle interactions which act as a decoherence process. The Quantum Boomerang effect is also present in higher dimensions, provided the dynamics is Anderson localized.