  As examples of quantum-"classical" coupling systems, multi-component systems
are studied by semiclassical evaluations of the Feynman kernels in the
coherent-state representation. From the observation of the phase space caustics
due to the presence of the internal degree of freedom (IDF), two phenomena are
explained in terms of the semiclassical theory: (1) The quantum oscillations of
the IDF induce quantum interference patterns in the Hushimi representation; (2)
Chaotic dynamics destroys the coherence of the quantum oscillations.
