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1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

Abstract : These notes describe a new method to investigate the spectral properties if quantum scattering Hamiltonians, developed in collaboration with J. Sjöstrand and M.Zworski. This method consists in constructing a family of -quantized transfer operators- $\{Mz,h\}$ associated with a classical Poincaré section near some fixed classical energy E. These operators are finite dimensional, and have the structure of -open quantum maps-. In the semiclassical limit, the family $\{Mz,h\}$ encode the quantum dynamics near the energy E. In particular, the quantum resonances of the form $E+z$, for $z=Oh$, are obtained as the roots of $\det1-Mz,h=0$.

keyword : quantum chaotic scattering transfer operator monodromy operator quantum resonance





Autor: Stéphane Nonnenmacher -

Fuente: https://hal.archives-ouvertes.fr/



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