NONCYCLIC GEOMETRIC PHASE, COHERENT STATES, AND THE TIME-DEPENDENT VARIATIONAL PRINCIPLE - APPLICATION TO COUPLED ELECTRON-NUCLEAR DYNAMICS

Kinematical and dynamical aspects of the noncyclic geometric phase for coherent states are analyzed. It is shown for Glauber and SU(2) coher ent states that the geometric phase obeys a geodesic closure rule asso ciated with the coset space of the respective Lie group. In the former case the geodesic is a straight line in phase space, while in the lat ter the geodesic is a great circle on the Bloch sphere (S-2). An alter native expression for the geometric phase is derived from the time-dep endent variational principle by making a specific choice of gauge. The noncyclic geometric phase is numerically calculated in a time-depende nt variational treatment of the Ex epsilon Jahn-Teller model first int roduced by Longuet-Higgins and co-workers. The electronic and nuclear degrees of freedom are parametrized by SU(2) and Glauber coherent stat es respectively. In particular, the adiabatic limit is studied and sho wn to yield the anticipated Berry geometric phase. [S1050-2947(97)0851 0-7].