31 research outputs found
Perturbative diagonalization for Maryland-type quasiperiodic operators with flat pieces
We consider quasiperiodic operators on Zd with unbounded monotone sampling functions ("Maryland-type"), which are not required to be strictly monotone and are allowed to have flat segments. Under several geometric conditions on the frequencies, lengths of the segments, and their positions, we show that these operators enjoy Anderson localization at large disorder
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
Convergence of perturbation series for unbounded monotone quasiperiodic operators
We consider a class of unbounded quasiperiodic Schrödinger-type operators on ℓ2(Zd) with monotone potentials (akin to the Maryland model) and show that the Rayleigh–Schrödinger perturbation series for these operators converges in the regime of small kinetic energies, uniformly in the spectrum. As a consequence, we obtain a new proof of Anderson localization in a more general than before class of such operators, with explicit convergent series expansions for eigenvalues and eigenvectors. This result can be restricted to an energy window if the potential is only locally monotone and one-to-one. A modification of this approach also allows the potential to be non-strictly monotone and have a flat segment, under additional restrictions on the frequencies
(Table 1) Chemical composition of a sample contaiting native aluminium, Core DM9-647, Northeast Pacific
Composition, structure and occurrence of native aluminium in bottom sediments of the Northeast Pacific at Station DM9-647 are reported
Quasi-conformal mappings and periodic spectral problems in dimension two
No description supplie