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

TL;DR

This paper derives Lieb-Thirring inequalities for non self-adjoint magnetic quantum Hamiltonians, providing bounds on eigenvalue distributions near the essential spectrum, advancing understanding of spectral properties in quantum physics.

Contribution

It introduces new Lieb-Thirring bounds for non self-adjoint perturbations of magnetic Schrödinger and Pauli operators, a novel extension in spectral analysis.

Findings

Established Lieb-Thirring inequalities for non self-adjoint operators

Provided bounds on eigenvalue distribution near the essential spectrum

Applied results to magnetic Schrödinger and Pauli 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{\"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.