Periodic chaotic billiards: Quantum-classical correspondence in energy space - art. no. 036206

We investigate the properties of eigenstates and local density of states (L DOS) for a periodic two-dimensional rippled billiard, focusing on their qua ntum-classical correspondence in energy representation. To construct the cl assical counterparts of LDOS and the structure of eigenstates (SES), the ef fects of the boundary are first incorporated (via a canonical transformatio n) into an effective potential, rendering the one-particle motion in the 2D rippled billiard equivalent to that of two interacting particles in ID geo metry, We show that classical counterparts of SES and LDOS in the case of s trong chaotic motion reveal quite a good correspondence with the quantum qu antities. We also show that the main features of the SES and LDOS can be ex plained in terms of the underlying classical dynamics, in particular, of ce rtain periodic orbits. On the other hand, statistical properties of eigenst ates and LDOS turn out to be different from those prescribed by random matr ix theory. We discuss the quantum effects responsible for the nonergodic ch aracter of the eigenstates and individual LDOS that seem to be generic for this type of billiards with a large number of transverse channels.