ANALYSIS OF DYNAMIC EFFECTS ON GEOMETRIC PHASE BY MEANS OF TIME-DEPENDENT VARIATIONAL PRINCIPLE

To examine dynamical effects on the geometric phase at the semi-classical level, we apply the technique of the time-dependent variational principle to simple models which typically exhibit the geometric phase effects discovered by Berry, namely, the Jaynes-Cummings model and the generalized harmonic oscillator model. Parameters are themselves dynamical variables in our models. Instead of integrating out the "fast" variables at the first stage, we derive the canonical equations of motion both for "fast" and "slow" variables without the adiabatic assumption. Using special solutions of the canonical equations, we requantize the systems by Einstein's condition, in which Berry's phase appearing as a correction for the Bohr-Sommerfeld condition is modified by the dynamical effects related to the slow degree of freedom.