SEMICLASSICAL FEATURES IN THE QUANTUM DESCRIPTION OF A DIRAC PARTICLEIN A CAVITY

The question of classical correspondence in the case of the Dirac equa tion has not been fully resolved as yet. In this paper, we consider Di rac particles in cavities of various shapes and provide numerical evid ence of the influence of periodic orbits in the quantal density of sta tes, d(E). Interestingly, the orbit lengths seem to be the same as in the (scalar) spinless case, though the associated phases in the period ic orbit sum for d(E) are in general different. We also study the spec tral fluctuations and find that statistical measures reflect an order- to-chaos transition in the underlying classical dynamics, similar to t hat seen in the scalar case. We provide a detailed study of the wave f unctions as well and find, apart from other characteristic features, t he existence of scarred states. Typical irregular eigenfunction compon ents,:however, exhibit contour splitting and have a Gaussian amplitude distribution.