Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1999-05-08
Nonlinear Sciences
Chaotic Dynamics
4 latex pages, 5 ps figures
Scientific paper
A scattering process can be described by suitably closing the system and considering the first return map from the entrance onto itself. This scattering map may be singular and discontinuous, but it will be measure preserving as a consequence of the recurrence theorem applied to any region of a simpler map. In the case of a billiard this is the Birkhoff map. The semiclassical quantization of the Birkhoff map can be subdivided into an entrance and a repeller. The construction of a scattering operator then follows in exact analogy to the classical process. Generically, the approximate unitarity of the semiclassical Birkhoff map is inherited by the S-matrix, even for highly resonant scattering where direct quantization of the scattering map breaks down.
de Almeida Alfredo M. Ozorio
Vallejos Raul O.
No associations
LandOfFree
Poincare's Recurrence Theorem and the Unitarity of the S matrix 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 Poincare's Recurrence Theorem and the Unitarity of the S matrix, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Poincare's Recurrence Theorem and the Unitarity of the S matrix will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-81474