From open quantum systems to open quantum maps

Stéphane Nonnenmacher (1) , Johannes Sjoestrand (2) , Maciej Zworski (3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 Department of Mathematics [Berkeley]

For a class of quantized open chaotic systems satisfying a natural dynamical assumption, we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite dimensional operators obtained by quantizing the Poincaré map associated with the flow near the set of trapped trajectories.

Mots clés: quantum chaotic scattering; resonances; fractal repeller; open quantum map

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Dynamique Chaotique [nlin.CD]

Stéphane Nonnenmacher, Johannes Sjoestrand, Maciej Zworski. From open quantum systems to open quantum maps. Communications in Mathematical Physics, 2011, 304 (1), pp.1-48. ⟨10.1007/s00220-011-1214-0⟩. ⟨hal-00474392v2⟩