Calogero model, deformed oscillators and the collapse
Velimir Bardek, Larisa Jonke, Stjepan Meljanac, and Marijan Milekovic
TL;DR
This paper explores the Calogero model and deformed oscillators at a specific interaction parameter, revealing a collapse phenomenon in the large-N limit through algebraic and collective-field analyses.
Contribution
It introduces an algebraic approach for finite systems and applies collective-field theory to analyze the large-N behavior at a critical parameter value.
Findings
Large-N limit leads to collapsing free particles
Special interaction parameter nu=-1/N causes system collapse
Algebraic and collective-field methods complement each other
Abstract
We discuss the behavior of the Calogero model and the related model of deformed oscillators with the S_N extended Heisenberg algebra for a special value of the constant of interaction/statistical parameter nu. The problem with finite number of deformed oscillators is analyzed in the algebraic approach, while collective-field theory has been used to investigate the large-N limit. In this limit, system reduces to a large number of collapsing (free) particles, for nu=-1/N.
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