Barrier-top resonances for non globally analytic potentials

Jean-Francois Bony (1) , Setsuro Fujiie (2) , Thierry Ramond (3) , Maher Zerzeri (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 Graduate School of Material Science
3 LMO - Laboratoire de Mathématiques d'Orsay
4 LAGA - Laboratoire Analyse, Géométrie et Applications

We give the semiclassical asymptotic of barrier-top resonances for Schrödinger operators on R n , n ≥ 1, whose potential is C ∞ everywhere and analytic at infinity. In the globally analytic setting, this has already been obtained in [6, 24]. Our proof is based on a propagation of singularities theorem at a hyperbolic fixed point that we establish here. This last result refines a theorem of [3], and its proof follows another approach.

Mots clés: semiclassical asymptotics; microlocal analysis; hyperbolic fixed point; propagation of singularities; Schrödinger operators

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

Jean-Francois Bony, Setsuro Fujiie, Thierry Ramond, Maher Zerzeri. Barrier-top resonances for non globally analytic potentials. Journal of Spectral Theory, 2019, 9 (1), pp.315-348. ⟨10.4171/JST/249⟩. ⟨hal-02400050⟩