94-323 P. Exner,P. Duclos

CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS (97K, latex) Oct 18, 94

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. Dirichlet Laplacian on smooth curved tubes in two and three dimensions is investigated. It is shown that if the tube is smooth and thin enough, and its curvature (and torsion in three dimensions) decay sufficiently rapidly, there is always a bound state below the bottom of the essential spectrum. A criterion for existence of these bound states and an upper bound to their number are derived. Furthermore, perturbation theory for these eigenvalues with respect to the tube diameter is constructed and some open questions are formulated.

Files: 94-323.tex