Quantum chaos for the vibrating rectangular billiard

We consider oscillations of the length and width in rectangular quantum bil liards, a two "degree-of-vibration" configuration. We consider several supe rpositon states and discuss the effects of symmetry (in terms of the relati ve values of the quantum numbers of the superposed states) on the resulting evolution equations and derive necessary conditions for quantum chaos for both separable and inseparable potentials. We extend this analysis to n-dim ensional rectangular parallelepipeds with two degrees-of-vibration. We prod uce several sets of Poincare maps corresponding to different projections an d potentials in the two-dimensional case. Several of these display chaotic behavior. We distinguish between four types of behavior in the present syst em corresponding to the separability of the potential and the symmetry of t he superposition states. In particular, we contrast harmonic and anharmonic potentials. We note that vibrating rectangular quantum billiards may be us ed as a model for quantum-well nanostructures of the stated geometry, and w e observe chaotic behavior without passing to the semiclassical ((h) over b ar --> 0) or high quantum-number limits.