From chaos to disorder in quasi-1D billiards with corrugated surfaces

We study chaotic properties of eigenstates depending on the degree of complexity in boundaries of a 2D periodic billiard. Main attention is paid to the situation when the motion of a classical particle is strongly chaotic. Our approach allows us to explore the transition from deterministic to disordered chaos, and to link chaos to the degree of ergodicity in eigenstates of the billiard. We have found that bouncing balls strongly reduce chaotic properties of eigenstates, thus leading to a serious problem in statistical description for global properties of eigenstates. A quite unexpected effect of rough surfaces on the form of eigenstates has been discovered and explained by a strong localization of a subset of eigenstates in the energy representation.