N particles on a line with 1/r² repulsion — an exactly solvable many-body system
Particles N6
Coupling g1.0
Trap ω1.0
Speed1.0
The Calogero-Moser system is a remarkable exactly integrable model: N particles on a line in a harmonic trap with pairwise 1/r² repulsion.
Hamiltonian: H = Σ pᵢ²/2 + ω²xᵢ²/2 + g²Σᵢ<ⱼ 1/(xᵢ−xⱼ)².
The system has N conserved quantities in involution. A stunning fact: the eigenvalue spacing of the Lax matrix L remains constant — shown in the lower panel.