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 Poincar\'e-sphere suppresses the effect. A spectroscopic transition experiment can independently verify the phase-avalanche magnitudes.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 Poincar\'e-sphere suppresses the effect. A spectroscopic transition experiment can independently verify the phase-avalanche magnitudes.

Physical Review AFeb 2, 20065 citations

Non-adiabatic Berry phase for periodic Hamiltonians

D J Moore, G E Stedman

Berry's (1984) formulation of the topological phase for periodic Hamiltonians is extended to the case of non-adiabatic evolution by proper choice of initial states. This restores a full parallel with the non-adiabatic formalism of Aharonov and Anandan (1987) for periodic orbits in a projective Hilbert space. The Berry phase for the novel example of a single electron in a rigidly rotating octahedral environment is calculated using both this formalism and that used previously by Aharonov and Anandan and by Page (1987).Berry's (1984) formulation of the topological phase for periodic Hamiltonians is extended to the case of non-adiabatic evolution by proper choice of initial states. This restores a full parallel with the non-adiabatic formalism of Aharonov and Anandan (1987) for periodic orbits in a projective Hilbert space. The Berry phase for the novel example of a single electron in a rigidly rotating octahedral environment is calculated using both this formalism and that used previously by Aharonov and Anandan and by Page (1987).

Journal of Physics A Mathematical and GeneralJun 7, 199056 citations

(>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 Poincar\'e-sphere suppresses the effect. A spectroscopic transition experiment can independently verify the phase-avalanche magnitudes.