BAND-STRUCTURE AND QUANTUM POINCARE SECTIONS OF A CLASSICALLY CHAOTICQUANTUM RIPPLED CHANNEL

We obtain the energy band spectra, eigenfunctions, and quantum Poincar e sections of a free particle moving in a two-dimensional channel boun ded by a periodically varying (ripple) wall and a hat wall. Classical Poincare sections show a generic transition from regular to chaotic mo tion as the size of the ripple is increased. The energy band structure is obtained for two representative geometries corresponding to a wide and a narrow channel. The comparison of numerical results with the le vel-splitting predictions of low-order quantum degenerate perturbation theory elucidate some aspects of the classical-quantum correspondence . For larger ripple amplitudes the conduction bands for narrow channel s become flat and nearly equidistant at low energies. Quantum-classica l correspondence is discussed with the aid of quantum Poincare (Husimi ) plots.