On a Schrödinger operator with a purely imaginary potential in the semiclassical limit

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

We consider the operator A h = −h 2 ∆ + iV in the semi-classical limit h → 0, where V is a smooth real potential with no critical points. We obtain both the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. We extend here previous results obtained for the Dirichlet realization of A h by removing significant limitations that were formerly imposed on V. In addition, we apply our techniques to the more general Robin boundary condition and to a transmission problem which is of significant interest in physical applications.

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. On a Schrödinger operator with a purely imaginary potential in the semiclassical limit. Communications in Partial Differential Equations, 2019, 44 (12), pp.1542-1604. ⟨10.1080/03605302.2019.1646281⟩. ⟨hal-02343844⟩