Calogero model, the collapse of matter, and the large-N limit
Velimir Bardek, Larisa Jonke, Stjepan Meljanac, Marijan Mileković · arXiv (Cornell University) · 2001
We discuss the behavior of the Calogero model for a special value of the constant of interaction/statistical parameter ν. The problem with finite number of Calogero particles is analyzed in the algebraic approach, while collectivefield theory has been used to investigate the large-N limit. For ν = −1/N, system reduces to a large number of collapsing (free) particles. PACS number(s): 03.65.Fd, 03.65.Sq, 05.30.Pr The (rational) Calogero [1] model describes N identical particles which interact through an inverse-square two-body interaction and are subjected to a common confining harmonic force. The inverse-square potential can be regarded as a pure statistical interaction [2] and the model maps to an ideal gas of particles obeying fractional statistics. In one dimension, the usual notion of exchange statistics is not well defined because the exchange necessarily involves scattering [3], but instead one can apply Haldane’s definition of exclusion statistics [4]. The model is completely integrable in both the classical and quantum case [5], and that