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

Diomba Sambou (1)

1 Facultad de Matemáticas [Santiago de Chile]

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 Schrödinger and Pauli with constant magnetic field of strength $b>0$. 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.

Mots clés: Lieb-Thirring type inequalities; non self-adjoint relatively compact perturbations of self-adjoint operators; magnetic Shrödinger and Pauli operators.

Domaines: Physique mathématique [math-ph]; Analyse fonctionnelle [math.FA]

Diomba Sambou. Quantitative bounds on the discrete spectrum of non self-adjoint quantum magnetic Hamiltonians. 2016. ⟨hal-00926769v4⟩