2010/01/22 by Nonnenmacher, Stéphane
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1001.4073
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" \M(z,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 \M(z,h)\ encode the quantum dynamics near the energy E. In particular, the quantum resonances of the form E+z, for z=O(h), are obtained as the roots of det(1-M(z,h))=0.