1,189 research outputs found
Index theorems on manifolds with straight ends
We study Fredholm properties and index formulas for Dirac operators over
complete Riemannian manifolds with straight ends. An important class of
examples of such manifolds are complete Riemannian manifolds with pinched
negative sectional curvature and finite volume
Remarks on "Resolving isospectral `drums' by counting nodal domains"
In [3] the authors studied the 4-parameter family of isospectral flat 4-tori
T^\pm(a,b,c,d) discovered by Conway and Sloane. With a particular method of
counting nodal domains they were able to distinguish these tori (numerically)
by computing the corresponding nodal sequences relative to a few explicit
tuples (a,b,c,d). In this note we confirm the expectation expressed in [3] by
proving analytically that their nodal count distinguishes any 4-tuple of
distinct positive real numbers.Comment: 5 page
On the discrete spectrum of spin-orbit Hamiltonians with singular interactions
We give a variational proof of the existence of infinitely many bound states
below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba
and Dresselhaus cases) perturbed by measure potentials thus extending the
results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007)
F113--F117.Comment: 10 pages; to appear in Russian Journal of Mathematical Physics
(memorial volume in honor of Vladimir Geyler). Results improved in this
versio
On semiclassical dispersion relations of Harper-like operators
We describe some semiclassical spectral properties of Harper-like operators,
i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and
position. The spectral region corresponding to the separatrices of the
classical Hamiltonian is studied for the case of integer flux. We derive
asymptotic formula for the dispersion relations, the width of bands and gaps,
and show how geometric characteristics and the absence of symmetries of the
Hamiltonian influence the form of the energy bands.Comment: 13 pages, 8 figures; final version, to appear in J. Phys. A (2004
Approximation by point potentials in a magnetic field
We discuss magnetic Schrodinger operators perturbed by measures from the
generalized Kato class. Using an explicit Krein-like formula for their
resolvent, we prove that these operators can be approximated in the strong
resolvent sense by magnetic Schrodinger operators with point potentials. Since
the spectral problem of the latter operators is solvable, one in fact gets an
alternative way to calculate discrete spectra; we illustrate it by numerical
calculations in the case when the potential is supported by a circle.Comment: 16 pages, 2 eps figures, submitted to J. Phys.
Heat kernels on curved cones
A functorial derivation is presented of a heat-kernel expansion coefficient
on a manifold with a singular fixed point set of codimension two. The existence
of an extrinsic curvature term is pointed out.Comment: 4p.,sign errors corrected and a small addition,uses JyTeX,MUTP/94/0
- …