There is no quantum chaos, in the sense of exponential sensitivity to initial conditions, but there are several novel quantum phenomena which reflect the presence of classical chaos. The study of these phenomena is quantum chaology.
The influence of quantum chaos on small atomic systems is reviewed. It now seems clear that chaos in the usually understood sense (e.g. exponential sensitivity to perturbations) is not found in isolated quantum systems. However, there are phenomena which appear only when the corresponding classical system is chaotic. The stability of the classical dynamics, in other words whether it is regular or chaotic, has a profound effect on the character of the corresponding quantum spectrum and wavefunctions.