On the spectrum of curved quantum waveguides

Details On the spectrum of curved quantum waveguides On the spectrum of curved quantum waveguides

2003-06-03

arxiv.org/abs/math-ph/0306008v2

Publ. RIMS, Kyoto University, 41 (2005), no. 3., 757-791.

Physics

Mathematical Physics

LaTeX, 33 pages, 2 figures; revised version (mildly shorten, added references); to appear in Publ. RIMS, Kyoto University

Scientific paper

The spectrum of the Laplace operator in a curved strip of constant width built along an infinite plane curve, subject to three different types of boundary conditions (Dirichlet, Neumann and a combination of these ones, respectively), is investigated. We prove that the essential spectrum as a set is stable under any curvature of the reference curve which vanishes at infinity and find various sufficient conditions which guarantee the existence of geometrically induced discrete spectrum. Furthermore, we derive a lower bound on the distance between the essential spectrum and the spectral threshold for locally curved strips. The paper is also intended as an overview of some new and old results on spectral properties of curved quantum waveguides.

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