Integrability and level crossing manifolds in a quantum Hamiltonian system

Details Integrability and level crossing manifolds in a quantum Hamiltonian system Integrability and level crossing manifolds in a quantum Hamiltonian system

1998-06-17

arxiv.org/abs/chao-dyn/9806021v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 3 figures

Scientific paper

10.1103/PhysRevE.58.5720

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 blocks of dimensionalities K=l(l+1)/2, l=1,2,... In the six-dimensional (6D) parameter space of this model, classical integrability is satisfied on a 5D hypersurface, and level crossings occur on 4D manifolds that are completely embedded in the integrability hypersurface except for some lower-D sub-manifolds. 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.

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