Scar Formation at the Edge of the Chaotic Region

Scars have been mostly studied in the semiclassical limit. In this regime the density of states is high, and often the scarring effect gets dispersed among many states, complicating the understanding of scar formation. The systematics of scar formation at a very elementary level, uncluttered by other irrelevant effects, is studied by intentionally going to the edge of the chaotic region. The transition from chaos to order is induced by decreasing the value of , and a series of broad avoided crossings marks the border between these two regions; scars then appear as mixing of the pairs of interacting wave functions.