Phase avalanches in near-adiabatic evolutions

In the course of slow, nearly adiabatic motion of a system, relative changes in the slowness can cause abrupt and high magnitude phase changes, phase avalanches, superimposed on the ordinary geometric phases. The generality of this effect is examined for arbitrary Hamiltonians and multicomponent (> 2) wave packets and is found to be connected (through the Blaschke term in the theory of analytic signals) to amplitude zeros in the lower half of the complex time plane. Motion on a nonmaximal circle on the Poincare-sphere suppresses the effect. A spectroscopic transition experiment can independently verify the phase-avalanche magnitudes.