Poincaré section decomposition for quantum scatterers

We consider here scatterers that may be modeled as a cavity with an entrance lead. The decomposition is achieved by sectioning the cavity and adding new leads, thus generating two new scatterers. So a resonant scatterer, whose S-matrix has sharp energy peaks, can be resolved into a pair of scatterers with smooth energy dependence. The resonant behaviour is concentrated in a spectral determinant obtained from a dissipative section map. The semiclassical limit of this theory coincides with the orbit resummation previously proposed by Georgeot and Prange. A numerical example for a semiseparable scatterer is investigated, revealing the accurate portrayal of the Wigner time delay by the spectral determinant.