Two-particle scattering theory for anyons

Korff, C. , Lang, G. and Schrader, R. (1999) Two-particle scattering theory for anyons. Journal of Mathematical Physics, 40, pp. 1831-1869.

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We consider potential scattering theory of a nonrelativistic quantum mechanical 2-particle system in R^2 with anyon statistics. Sufficient conditions are given which guarantee the existence of wave operators and the unitarity of the S-matrix. As examples the rotationally invariant potential well and the delta-function potential are discussed in detail. In case of a general rotationally invariant potential the angular momentum decomposition leads to a theory of Jost functions. The anyon statistics parameter gives rise to an interpolation for angular momenta analogous to the Regge trajectories for complex angular momenta. Levinson's theorem is adapted to the present context. In particular we find that in case of a zero energy resonance the statistics parameter can be determined from the scattering phase.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Korff, Professor Christian
Authors: Korff, C., Lang, G., and Schrader, R.
Subjects:Q Science > QA Mathematics
Q Science > QC Physics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Research Group:Integrable Systems and Mathematical Physics
Journal Name:Journal of Mathematical Physics

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