Scattering of clusters in quantum calogero model
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 2, pp. 341-347
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It is well known that scattering of particles in the Calogero model, which recently drew attention in connection with $c=1$ strings and integrable models in statistical mechanics, is reduced to
two-particle collisions. It follows from Harish-Chandra and Gindikin–Karpelevich results, related to the harmonic analysis on simple Lie groups. Unfortunately their formulae don't work if particles form clusters in the asymptotics. We reformulate their results in a form which
allows to apply them to this situation. The scattering of clusters is also factorizible, but depends on structures of constituents. In conclusion we discuss a similar problem in the deformed Calogero model related to quantum groups, which describes also interactions of excited states
in the XXZ-model.
@article{TMF_1993_95_2_a16,
author = {M. A. Olshanetsky},
title = {Scattering of clusters in quantum calogero model},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {341--347},
publisher = {mathdoc},
volume = {95},
number = {2},
year = {1993},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1993_95_2_a16/}
}
M. A. Olshanetsky. Scattering of clusters in quantum calogero model. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 2, pp. 341-347. http://geodesic.mathdoc.fr/item/TMF_1993_95_2_a16/