Quantum chaos for the radially vibrating spherical billiard

The spherical quantum billiard with a time-varying radius, a(t), is conside red. It is proved that only superposition states with components of common rotational symmetry give rise to chaos. Examples of both nonchaotic and cha otic states are described. In both cases, a Hamiltonian is derived in which a and P are canonical coordinate and momentum, respectively. For the chaot ic case, working in Bloch variables (x,y,z), equations describing the motio n are derived. A potential function is introduced which gives bounded motio n of a(t). Poincare maps of (a,P) at x=0 and the Bloch sphere projected ont o the (x,y) plane at P=0 both reveal chaotic characteristics. (C) 2000 Amer ican Institute of Physics. [S1054-1500(00)00602-9].