Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Eigenvalue asymptotics of perturbed periodic Dirac systems in the slow-decay limit

Author(s): Karl Michael Schmidt
Journal: Proc. Amer. Math. Soc. 131 (2003), 1205-1214.
MSC (2000): Primary 34L20, 34L40, 47E05, 81Q10, 81Q15
Posted: July 26, 2002
MathSciNet review: 1948112
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Abstract: A perturbation decaying to at $\infty$ and not too irregular at introduces at most a discrete set of eigenvalues into the spectral gaps of a one-dimensional Dirac operator on the half-line. We show that the number of these eigenvalues in a compact subset of a gap in the essential spectrum is given by a quasi-semiclassical asymptotic formula in the slow-decay limit, which for power-decaying perturbations is equivalent to the large-coupling limit. This asymptotic behaviour elucidates the origin of the dense point spectrum observed in spherically symmetric, radially periodic three-dimensional Dirac operators.

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