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We consider a two-spin model, represented classically by a nonlinear autonomous Hamiltonian system with two degrees of freedom and a nontrivial integrability condition, and quantum mechanically by a real symmetric Hamiltonian matrix with invariant blocks of dimensionalities K = 1/ l(l+1), l = 1, 2,…. In the six-dimensional parameter space of this model, classical integrability is satisfied on a five-dimensional hypersurface, and level crossings occur on four-dimensional manifolds that are completely embedded in the integrability hypersurface except for some lower-dimensional submanifolds. Under mild assumptions, the classical integrability condition can be reconstructed from a purely quantum mechanical study of level degeneracies in finite-dimensional invariant blocks of the Hamiltonian matrix. Our conclusions are based on rigorous results for K = 3 and on numerical results for K = 6,10.
V.V. Stepanov and G. Müller. Integrability and level crossing manifolds in quantum Hamiltonian system. Physical Review E, 58(1998), 5720-5726.
Available at: http://dx.doi.org/10.1103/PhysRevE.58.5720