Geometric quantization of mechanical systems with time-dependent parameters.

Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modem holonomic quantum computation. We here provide complete geometric quantization of a Hamiltonian system with time-dependent parameters, without the adiabatic assumption. A Hamiltonian of such a system is affine in the temporal derivative of parameter functions. This leads to the geometric Berry factor phenomena. [ABSTRACT FROM AUTHOR]