Eigenvalue Asymptotics in a Twisted Waveguide
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
TAYLOR & FRANCIS INC
Abstract
We consider a twisted quantum wave guide i.e., a domain of the form :=r x where 2 is a bounded domain, and r=r(x3) is a rotation by the angle (x3) depending on the longitudinal variable x3. We are interested in the spectral analysis of the Dirichlet Laplacian H acting in L2(). We suppose that the derivative [image omitted] of the rotation angle can be written as [image omitted](x3)=-epsilon(x3) with a positive constant and epsilon(x3) L|x3|-, |x3|. We show that if L0 and (0,2), or if LL00 and =2, then there is an infinite sequence of discrete eigenvalues lying below the infimum of the essential spectrum of H, and obtain the main asymptotic term of this sequence.
Description
Keywords
Eigenvalue asymptotics, Schrodinger operators, Waveguides, SCHRODINGER OPERATOR