Quantum scars of classical orbits in small interacting electronic systems

The scarring by classical orbits of the electron density of small two-dimensional interacting electronic systems is studied. The ground state of the system is analyzed semiclassically using the Kohn-Sham equations and the local density approximation. This analysis associates the Friedel oscillations with classical orbits of a particle moving in some effective potential. These are the orbits that bounce from the boundary of the potential once. New density oscillations, associated with short periodic orbits, emerge as an extension of this picture. These are the many-body counterpart of “scars” found in single-particle eigenstates. It is shown that scarring can take place when the disorder is weak and the electron density is sufficiently high.