Saddle scars: Existence and applications

Abstract

A quantum scar is a wave function which displays an high intensity in the region of a classical unstable periodic orbit. Saddle scars are states related to the unstable harmonic motions along the stable manifold of a saddle point of the potential. Using a semiclassical method it is shown that, independently of the overall structure of the potential, the local dynamics of the saddle point is sufficient to insure the general existence of this type of scars and their factorized structure is obtained. Potentially useful situations are identified, where these states appear (directly or in disguise) and might be used for quantum control purposes.