Dirichlet and Neumann eigenvalues for half-plane magnetic Hamiltonians
Language
en
Article de revue
This item was published in
Reviews in Mathematical Physics. 2014, vol. 26, n° 2, p. 1450003
World Scientific Publishing
English Abstract
Let H-0,(D) (respectively, H-0,H-N) be the Schrodinger operator in constant magnetic field on the half-plane with Dirichlet (respectively, Neumann) boundary conditions, and let H-l := H-0,H-l - V, l = D, N, where the scalar ...Read more >
Let H-0,(D) (respectively, H-0,H-N) be the Schrodinger operator in constant magnetic field on the half-plane with Dirichlet (respectively, Neumann) boundary conditions, and let H-l := H-0,H-l - V, l = D, N, where the scalar potential V is non-negative, bounded, does not vanish identically, and decays at infinity. We compare the distribution of the eigenvalues of H-D and H-N below the respective infima of the essential spectra. To this end, we construct effective Hamiltonians which govern the asymptotic behavior of the discrete spectrum of Hl near inf sigma(ess)(H-l) = inf sigma(H-0,H-l), l = D, N. Applying these Hamiltonians, we show that sigma(disc)(H-D) is infinite even if V has a compact support, while sigma(disc)(H-N) could be finite or infinite depending on the decay rate of VRead less <
Origin
Hal imported