Semiclassical resolvent estimates in chaotic scattering

Stéphane Nonnenmacher (1) , Maciej Zworski (2)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 Department of Mathematics [Berkeley]

In this short note we prove a resolvent estimate in the pole free strip for certain Schrödinger-type operators whose classical Hamiltonian flows are assumed to be hyperbolic on the trapped set which is assumed to be sufficiently filamentary.

Mots clés: quantum chaotic scattering; resonances; fractal repeller

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Systèmes dynamiques [math.DS]; Equations aux dérivées partielles [math.AP]

Stéphane Nonnenmacher, Maciej Zworski. Semiclassical resolvent estimates in chaotic scattering. 2009. ⟨hal-00376771v2⟩