Quantum Three Wave Interaction Models: Bethe Ansatz and Statistical Mechanics
The Bethe Ansatz method was first used by Bethe to obtain the eigenstates of the Hamiltonian for the spin wave problem . This method is also valid for many other models such as the quantum nonlinear Schrödinger model (delta-function interaction model) , the massive Thirring model , etc.. C.N.Yang and C.P.Yang exploit this method, and succeed in getting the equilibrium of the thermodynamics of the system with a finite temperature . We find that the eigenstates of the quantum three wave interaction model can be derived by the Bethe Ansatz method . We treat the thermodynamics in the case without the bound states in the eigenstates, as some difficulties occur with the existence of the bound states.
KeywordsFinite Temperature Hole Density Fermion Model Quantum Inverse Large Volume Limit
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