Limiting absorption principle for some long range perturbations of Dirac systems at threshold energies

Nabile Boussaid (1) , Sylvain Golénia (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 Mathematisches Institut der Universität Erlangen-Nürnberg

We establish a limiting absorption principle for some long range perturbations of the Dirac systems at threshold energies. We cover multi-center interactions with small coupling constants. The analysis is reduced to study a family of non-self-adjoint operators. The technique is based on a positive commutator theory for non self-adjoint operators, which we develop in appendix. We also discuss some applications to the dispersive Helmholzt model in the quantum regime.

Mots clés: Coulomb-Dirac; thresholds; positive commutator estimate; resolvent estimates; limiting absorption principle; Helmholtz; non selfadjoint operators; selfadjoint operators

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Théorie spectrale [math.SP]

Nabile Boussaid, Sylvain Golénia. Limiting absorption principle for some long range perturbations of Dirac systems at threshold energies. 2009. ⟨hal-00392422⟩