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

2014/02/10 by Diomba Sambou, Sambou, Diomba
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.FA #math.MP

paper · pdf · doi:10.48550/arxiv.1402.2265

11 pages

arxiv created 2016/03/15 · arxiv updated 2016/03/16

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 Schrödinger and Pauli with constant magnetic field of strength b\textgreater0. 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.

Related

• Lieb-Thirring type inequalities for non self-adjoint perturbations of magnetic Schrödinger operators
• Spectral non-self-adjoint analysis of complex Dirac, Pauli and Schrödinger operators of full rank with constant magnetic fields
• Remarks on eigenvalue estimates and semigroup domination
• On a quantum Hamiltonian in a unitary magnetic field with axisymmetric potential
• On eigenvalue accumulation for non-self-adjoint magnetic operators