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

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

2001-11-09

arxiv.org/abs/math/0111115v1

Mathematics

Spectral Theory

Scientific paper

A perturbation decaying to 0 at infinity and not too irregular at 0 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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