Multicomponent Calogero Model of $B_N$-Type Confined in Harmonic Potential

Abstract

A new one-dimensional model, the multicomponent Calogero model of $B_N$-type confined in the harmonic potential, is introduced. The Lax pair of this model is determined, and then a set of functionally independent conserved operators are constructed. Moreover, the energy spectrums of the above model are obtained by three different methods.

15 pages, REVTeX3

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Cited by in corpus (34)

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• Supersymmetry, Shape Invariance and Solvability of $A_{N-1}$ and $B{C}_N$ Calogero-Sutherland Model
• Integrable $1/r^2$ Spin Chain with Reflecting End
• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Exactly solvable D_N-type quantum spin models with long-range interaction
• Inozemtsev's hyperbolic spin model and its related spin chain
• On R-matrix valued Lax pairs for Calogero-Moser models
• An exactly solvable three-particle problem with three-body interaction
• The spin Sutherland model of D_N type and its associated spin chain
• Universal Lax pairs for Spin Calogero-Moser Models and Spin Exchange Models
• Solvable scalar and spin models with near-neighbors interactions
• The exactly solvable spin Sutherland model of B_N type and its related spin chain
• Integrable open spin chains related to infinite matrix product states
• New Non-Symmetric Orthogonal Basis for the Calogero Model with Distinguishable Particles
• Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
• Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models
• Integrable coupled Li$\acute{e}$nard-type systems with balanced loss and gain
• Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• $W_{1+\infty }$ constraints for the hermitian one-matrix model
• Intertwining Operators for a Degenerate Double Affine Hecke Algebra and Multivariable Orthogonal Polynomials
• Algebraic study on the $A_{N-1}$- and $B_N$-Calogero models with bosonic, fermionic and distinguishable particles
• Hierarchies of Spin Models related to Calogero-Moser Models
• Planar Harmonic Polynomials of Type B
• Three-body generalization of the Sutherland model with internal degrees of freedom
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• A novel class of translationally invariant spin chains with long-range interactions
• The open Haldane-Shastry chain: thermodynamics and criticality
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
• On the maximal superintegrability of strongly isochronous Hamiltonians
• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid