Stokes phase and geometrical phase in a driven two-level system

The generic two-level model with time-dependent matrix elements becomes soluble in the limit that its diagonal and off-diagonal terms vary along a flat ellipse, encircling the diabolical singular point in the parameter space. The time evolution of the state vector is explicitly obtained, and the condition for its evolution to form a closed circuit in the projective Hilbert space of rays is given as a result of destructive interference at level crossing. The Aharonov-Anandan geometrical phase is shown to be related to the Stokes phase for the Landau-Zener model, which is a natural extension of Berry's phase to nonadiabatic evolutions.