We generalize the concept of level spacings to dissipative quantum maps. For periodically kicked tops with damping, we find linear and cubic level repulsions under conditions of classically regular and chaotic motion, respectively. The numerically obtained spacing distribution for the chaotic top appears to be universal: It compares favorably with the spacing distribution of general complex matrices of large dimension, the analytical form of which we also present.

• Received 16 May 1988

DOI:https://doi.org/10.1103/PhysRevLett.61.1899