A Note on Dressed S-Matrices in Models with Long-Range Interactions

Abstract

The {\sl dressed} Scattering matrix describing scattering of quasiparticles in various models with long-range interactions is evaluated by means of Korepin's method\upref vek1/. For models with $\frac{1}{{\sin }^2(r)}$-interactions the S-matrix is found to be a momentum-independent phase, which clearly demonstrates the ideal gas character of the quasiparticles in such models. We then determine S-matrices for some models with $\frac{1}{{\sinh }^2(r)}$-interaction and find them to be in general nontrivial. For the $\frac{1}{r^2}$-limit of the $\frac{1}{{\sinh }^2(r)}$-interaction we recover trivial S-matrices, thus exhibiting a crossover from interacting to noninteracting quasiparticles. The relation of the S-matrix to fractional statistics is discussed.

18 pages, jyTeX (macro included - just TeX the file) BONN-TH-94-13, revised version: analysis of models with 1/sinh^2 interaction added

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