Quantum chaos for the radially vibrating spherical billiard

The spherical quantum billiard with a time-varying radius, a(t), is considered. It is proved that only superposition states with components of common rotational symmetry give rise to chaos. Examples of both nonchaotic and chaotic states are described. In both cases, a Hamiltonian is derived in which a and P are canonical coordinate and momentum, respectively. For the chaotic case, working in Bloch variables (x,y,z), equations describing the motion are derived. A potential function is introduced which gives bounded motion of a(t). Poincare maps of (a,P) at x=0 and the Bloch sphere projected onto the (x,y) plane at P=0 both reveal chaotic characteristics. (c) 2000 American Institute of Physics.