Spectral semi-classical analysis of a complex Schrödinger operator in exterior domains

Y. Almog (1) , Denis S Grebenkov (2) , B. Helffer (3)

1 LSU - Louisiana State University
2 LPMC - Laboratoire de physique de la matière condensée
3 LMJL - Laboratoire de Mathématiques Jean Leray

Generalizing previous results obtained for the spectrum of the Dirichlet and Neumann realizations in a bounded domain of a Schrödinger operator with a purely imaginary potential −h 2 ∆ + iV in the semiclassical limit h → 0 we address the same problem in exterior domains. In particular we obtain the left margin of the spectrum, and the emptiness of the essential part of the spectrum under some additional assumptions.

Domaines: Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]; Biophysique [physics.bio-ph]; Chimie-Physique [physics.chem-ph]; Physique Numérique [physics.comp-ph]; Analyse de données, Statistiques et Probabilités [physics.data-an]

Y. Almog, Denis S Grebenkov, B. Helffer. Spectral semi-classical analysis of a complex Schrödinger operator in exterior domains. Journal of Mathematical Physics, 2018, 59 (4), pp.041501. ⟨10.1063/1.4999625⟩. ⟨hal-02344206⟩