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. (C) 2001 Elsevier Science B.V. All rights reserved. [References: 9]
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