- 02-200 David Krejcirik
- Quantum strips on surfaces
Apr 26, 02
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Abstract. Motivated by the theory of quantum waveguides,
we investigate the spectrum of the Laplacian,
subject to Dirichlet boundary conditions,
in a curved strip of constant width
that is defined as a tubular neighbourhood
of an infinite curve in a two-dimensional Riemannian manifold.
Under the assumption that the strip is asymptotically
straight in a suitable sense, we localise the essential
spectrum and find sufficient conditions which
guarantee the existence of geometrically induced
bound states. In particular, the discrete spectrum exists
for non-negatively curved strips which are studied
in detail. The general results are used to recover
and revisit the known facts about quantum strips in the plane.
As an example of non-positively curved
quantum strips, we consider strips on ruled surfaces.