Regularity in nonlinearly coupled quantum oscillators far from the semiclassical limit

The amount of regularity of classical trajectories and quantum states of a two-dimensional anharmonic oscillator far from the semiclassical limit are compared. It is found for this model system that the degree of regularity is considerably higher for the quantum system and that the amount of regularity of the quantum system increases with increasing energy in the high-energy region while the classical system shows the opposite trend.