Discrete spectrum of cranked quantum and elastic waveguides


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Resumo

The spectrum of quantum and elastic waveguides in the form of a cranked strip is studied. In the Dirichlet spectral problem for the Laplacian (quantum waveguide), in addition to well-known results on the existence of isolated eigenvalues for any angle α at the corner, a priori lower bounds are established for these eigenvalues. It is explained why methods developed in the scalar case are frequently inapplicable to vector problems. For an elastic isotropic waveguide with a clamped boundary, the discrete spectrum is proved to be nonempty only for small or close-to-π angles α. The asymptotics of some eigenvalues are constructed. Elastic waveguides of other shapes are discussed.

Sobre autores

S. Nazarov

St. Petersburg State University; St. Petersburg State Polytechnical University; Institute of Problems of Mechanical Engineering

Autor responsável pela correspondência
Email: srgnazarov@yahoo.co.uk
Rússia, Universitetskii pr. 28, Staryi Peterhof, St. Petersburg, 198504; Politekhnicheskaya ul. 29, St. Petersburg, 195251; Bolshoi pr. 61, V.O., St. Petersburg, 199178

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