State scarring by ‘‘ghosts’’ of periodic orbits

In this paper we discover a generic structure in the eigenfunctions of quantum billiards, namely, scarring by families of stable periodic orbits in a nonchaotic system. Our study is conducted on two different triangular billiards, one an ergodic system and the other a ‘‘pseudointegrable’’ billiard. Surprisingly, we detect scars in regions which contain no periodic orbits. The periodic orbits responsible for scarring reside in a ‘‘neighboring’’ triangle. Such orbits show a more complex phase space structure than the ‘‘bouncing ball’’ trajectories of the stadium billiard. While diffuse nodal structure is usually the antithesis of scarring, we show that in some eigenstates it is supported by extensive families of stable periodic orbits.