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arXiv · 1402.2265

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

Diomba Sambou
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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{\"o}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.

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Diomba Sambou. 2014-02-10. Quantitative bounds on the discrete spectrum of non self-adjoint quantum magnetic Hamiltonians. https://arxiv.org/abs/1402.2265

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