Quantum transfer operators and quantum scattering

Details Quantum transfer operators and quantum scattering Quantum transfer operators and quantum scattering

2010-01-22

arxiv.org/abs/1001.4073v1

Physics

Mathematical Physics

18 pages, 3 figures

Scientific paper

These notes describe a new method to investigate the spectral properties if quantum scattering Hamiltonians, developed in collaboration with J. Sj\"ostrand and M.Zworski. This method consists in constructing a family of "quantized transfer operators" $\{M(z,h)\}$ associated with a classical Poincar\'e 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 $\det(1-M(z,h))=0$.

Affiliated with

Also associated with

No associations

Rating

Quantum transfer operators and quantum scattering does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum transfer operators and quantum scattering, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum transfer operators and quantum scattering will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-514502