Physics NotePublished
Poincaré's Recurrence Theorem and the Unitarity of the S-Matrix
A. M. Ozorio de Almeida; R. O. Vallejos
1997
Publication details
- Authors
- A. M. Ozorio de Almeida; R. O. Vallejos
- Type
- Physics Note
- Status
- Published
- Publication date
- 1997
- Description
- 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. Unitarity of the Birkhoff map implies that this scattering operator is itself unitary, as a consequence of a quantized version of the recurrence theorem.
- Year
- 1997
- Number
- CBPF-NF-064/97
- Linked to a thesis
- No
- Linked to a grant
- No