Absolute continuity of a two-dimensional magnetic periodic Schr\"odinger operator with measure derivative like potential

R. G. Shterenberg

Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 31, Tome 271 (2000), pp. 276-312

Résumé

A two-dimensional magnetic periodic Schrödinger operator with variable metric is considered. Electric potential is suggested to be a distribution formally given by the expression $\frac{d\nu}{d\bold x}$, where $d\nu$ is a periodic measure with locally finite variation. We assume that the perturbation generated by electric potential is strongly subordinate (in the sense of forms) to the free operator. Under this natural assumption, we prove the absolute continuity of the spectrum of the Schrödinger operator.