artículo
Spectral properties of a magnetic quantum Hamiltonian on a strip
Fecha
2008Registro en:
10.3233/ASY-2008-0875
0921-7134
WOS:000258079800001
Autor
Briet, Philippe
Raikov, Georgi
Soccorsi, Eric
Institución
Resumen
We consider a 2D Schrodinger operator H(0) with constant magnetic field, on a strip of finite width. The spectrum of H(0) is absolutely continuous, and contains a discrete set of thresholds. We perturb H(0) by an electric potential V which decays in a suitable sense at infinity, and study the spectral properties of the perturbed operator H = H(0) + V. First, we establish a Mourre estimate, and as a corollary prove that the singular continuous spectrum of H is empty, and any compact subset of the complement of the threshold set may contain at most a finite set of eigenvalues of H, each of them having a finite multiplicity. Next, we introduce the Krein spectral shift function (SSF) for the operator pair (H, H(0)). We show that this SSF is bounded on any compact subset of the complement of the threshold set, and is continuous away from the threshold set and the eigenvalues of H. The main results of the article concern the asymptotic behaviour of the SSF at the thresholds, which is described in terms of the SSF for a pair of effective Hamiltonians.