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Quantum chaology in the discrete self-trapping equation in the presence of Arnold diffusion

A generalised discrete self-trapping equation with four degrees of freedom is investigated classically and quantum mechanically. The presence of Arnold diffusion enables a numerical test of a semiclassical conjecture by Berry and Robnik. Our results confirm the conjecture in almost regular and strongly chaotic regions of phase space. In the weakly chaotic regions a possible failure of the conjecture should not be overlooked.