Perturbation-Induced Quantum Scars

The scarring of a single-particle wave function is one of the most striking phenomena in the field of quantum chaos. In consequence of quantum interference, the probability density of a quantum state can be concentrated along short unstable periodic orbits of the corresponding chaotic classical system, and the quantum state bears an imprint of the orbit – a quantum scar. In addition to this conventional scarring, we here consider a new class of quantum scars: some of the high-energy eigenstates of a locally perturbed quantum well are strongly scarred by the periodic orbits of the unperturbed classical counterpart. This perturbation-induced scarring emerges as a combination of near-degenerate states in the unperturbed system and the localized nature of the perturbation. Besides being a striking visualization of quantum-mechanical suppression of classical chaos, the existence, geometry and orientation of the scars are highly controllable. In addition, these kind of scars can be exploited to propagate quantum wave packets in the perturbed system with very high fidelity, thus paving a way towards new experimental schemes to manipulate electronic current in two-dimensional nanostructures. In particular, the generality of the presented scarring mechanism indicates that these new scars may be much more common in disordered quantum systems than previously thought.