Geometrically induced spectrum in curved leaky wires
نویسنده
چکیده
The aim of the present paper is to elucidate some geometrically induced spectral properties for the Laplacian in L(R) perturbed by a negative multiple of the Dirac measure of an infinite curve Γ in the plane. This problem has at least two motivations. On the physics side we note that quantum mechanics of electrons confined to narrow tubelike regions has attracted a considerable interest, because such systems represent a natural model for semiconductor “quantum wires”. In some examples the region in question is a strip or tube with hard walls – see, e.g., [DE] and references therein – while other treatments assume even stronger localization to a curve
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