Quantitative bounds on the discrete spectrum of non self-adjoint quantum magnetic Hamiltonians

Abstract

We establish Lieb-Thirring type inequalities for non self-adjoint relatively compact perturbations of certain operators of mathematical physics. We apply our results to quantum Hamiltonians of Schr{ö}dinger and Pauli with constant magnetic field of strength $b\textgreater{}0$. In particular, we use these bounds to obtain some information on the distribution of the eigenvalues of the perturbed operators in the neighborhood of their essential spectrum.

11 pages

References in corpus (2)

• Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
• Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators