P. Exner, M. Fraas
Interlaced dense point and absolutely continuous
spectra for Hamiltonians with concentric-shell singular
interactions
(48K, LaTeX)
ABSTRACT. We analyze the spectrum of the generalized Schrodinger operator
in $L^2(R^\nu) \nu \geq 2$, with a general local,
rotationally invariant singular interaction supported by an
infinite family of concentric, equidistantly spaced spheres. It is
shown that the essential spectrum consists of interlaced segments
of the dense point and absolutely continuous character, and that
the relation of their lengths at high energies depends on the
choice of the interaction parameters; generically the p.p.
component is asymptotically dominant. We also show that for
$\nu=2$ there is an infinite family of eigenvalues below the
lowest band.