On the solution of the Calogero model for distinguishable particles in the domain of intermediate statistics

A multispecies Calogero model

“…( 2) trivially vanishes. When ν ij are mutually different but m i = m, ∀i, we recover the model treated in [11,13]. Finally, when ν ij = αm i m j , α being constant, we obtain the model mentioned in [10,12].…”

“…In this way we obtain a 1D multispecies Calogero model. Very little is known about its spectra and wavefunctions [10][11][12][13].…”

“…We also establish the necessary conditions for the equivalence of the two multispecies Calogero models. In Section 4 we briefly repeat the main points of the paper and make contact with the models studied in [10][11][12][13].…”

Calogero Model(s) and Deformed Oscillators

“…Nevertheless, this algebraic approach still reproduces correctly some of the excited states. There is a claim in the literature [35], based on numerical and perturbative analysis of the 3-particle model, that there is no algebra of raising and lowering operators for the multispecies model which gives its complete spectrum. At the moment, we cannot prove or disproves this claim.…”

Fun and frustration with Calogero model

“…Nevertheless, this algebraic approach still reproduces correctly some of the excited states. There is even a claim in the literature [9], based on numerical and perturbative analysis of the multispecies 3-particle model, that there is no algebra of raising and lowering operators which gives its complete spectrum.…”