We study the formation of long-lived states near avoided resonance crossings
in open systems. For three different optical microcavities (rectangle, ellipse,
and semi-stadium) we provide numerical evidence that these states are localized
along periodic rays, resembling scarred states in closed systems. Our results
shed light on the morphology of long-lived states in open mesoscopic systems.Comment: 4 pages, 5 figures (in reduced quality), to appear in Phys. Rev. Let