A DIRAC SEA AND THERMODYNAMIC-EQUILIBRIUM FOR THE QUANTIZED 3-WAVE INTERACTION

The classical version of the three-wave interaction models the creatio n and destruction of waves; the quantized version models the creation and destruction of particles. The quantum three-wave interaction is de scribed and the Bethe ansatz for the eigenfunctions is given in closed form. The Bethe equations are derived in a rigorous fashion and are s hown to have a thermodynamic limit. The Dirac sea of negative energy s tates is obtained as the infinite density limit. Finite particle/hole excitations are determined and the asymptotic relation of energy and m omentum is obtained. The Yang-Yang functional for the relative free en ergy of finite density excitations is constructed and is shown to be c onvex and bounded below. The equations of thermal equilibrium are obta ined. (C) 1998 American Institute of Physics.