2014/08/09 by Diomba Sambou, Sambou, Diomba
Computer Science · Materials Science · Mathematics · #FOS: Mathematics #FOS: Physical sciences #Magnetism in coordination complexes #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1408.2109
openalex publication_date 2014/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Dirac, Pauli and Schrödinger quantum magnetic Hamiltonians of full rank in \rm L2 (ℝ2d ), d ≥ 1, perturbed by non-self-adjoint (matrix-valued) potentials. On the one hand, we show the existence of non-self-adjoint perturbations, generating near each point of the essential spectrum of the operators, infinitely many (complex) eigenvalues. In particular, we establish point spectrum analogous of Bögli results [Bög17] obtained for non-magnetic Laplacians, and hence showing that classical Lieb-Thirring inequalities cannot hold for our magnetic models. On the other hand, we give asymptotic behaviours of the number of the (complex) eigenvalues. In particular, for compactly supported potentials, our results establish non-self-adjoint extensions of Raikov-Warzel [RW02] and Melgaard-Rozenblum [MR03] results. So, we show how the (complex) eigenvalues converge to the points of the essential spectrum asymptotically, i.e., up to a multiplicative explicit constant, as (1)/(d!) ((\vert ln r \vert)/(ln \vert ln r \vert) )d, r \searrow 0, in small annulus of radius r > 0 around the points of the essential spectrum.