15 research outputs found
Eigenvalues of Laplacian with constant magnetic field on non-compact hyperbolic surfaces with finite area
We consider a magnetic Laplacian on a
noncompact hyperbolic surface \mM with finite area. is a real one-form
and the magnetic field is constant in each cusp. When the harmonic
component of satifies some quantified condition, the spectrum of
is discrete. In this case we prove that the counting function of
the eigenvalues of satisfies the classical Weyl formula, even
when $dA=0.
Zero modes in a system of Aharonov-Bohm fluxes
We study zero modes of two-dimensional Pauli operators with Aharonov--Bohm
fluxes in the case when the solenoids are arranged in periodic structures like
chains or lattices. We also consider perturbations to such periodic systems
which may be infinite and irregular but they are always supposed to be
sufficiently scarce
On absolute continuity of the spectrum of a periodic magnetic Schr\"odinger operator
We consider the Schr\"odinger operator in , , with
the electric potential and the magnetic potential being periodic
functions (with a common period lattice) and prove absolute continuity of the
spectrum of the operator in question under some conditions which, in
particular, are satisfied if
and , .Comment: 25 page