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Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator

We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic...

Resonances and Spectral Shift Function near the Landau levels

Jean-François BonyVincent BruneauGeorgi Raikov — 2007

Annales de l’institut Fourier

We consider the 3D Schrödinger operator H = H 0 + V where H 0 = ( - i - A ) 2 - b , A is a magnetic potential generating a constant magneticfield of strength b > 0 , and V is a short-range electric potential which decays superexponentially with respect to the variable along the magnetic field. We show that the resolvent of H admits a meromorphic extension from the upper half plane to an appropriate Riemann surface , and define the resonances of H as the poles of this meromorphic extension. We study their distribution near any fixed...

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