A quantum scar - an enhancement of a quantum probability density in the
vicinity of a classical periodic orbit - is a fundamental phenomenon connecting
quantum and classical mechanics. Here we demonstrate that some of the
eigenstates of the perturbed two-dimensional anisotropic (elliptic) harmonic
oscillator are strongly scarred by the Lissajous orbits of the unperturbed
classical counterpart. In particular, we show that the occurrence and geometry
of these quantum Lissajous scars are connected to the anisotropy of the
harmonic confinement, but unlike the classical Lissajous orbits the scars
survive under a small perturbation of the potential. This Lissajous scarring is
caused by the combined effect of the quantum (near) degeneracies in the
unperturbed system and the localized character of the perturbation.
Furthermore, we discuss experimental schemes to observe this
perturbation-induced scarring.Comment: 6 pages, 3 figure
