For 10 points, identify this quantity, a phase factor acquired by a particle in such experiments as the Aharonov-Bohm experiment.
This quantity is now used to explain the anomalous velocity that appears in Karplus and Luttinger's theory of the anomalous Hall effect. The numbers introduced to study the quantum Hall effect by Thouless et al. were interpreted using the ideas behind this quantity in terms of eigenvalue degeneracies in an one article; that article also identifies this quantity as a holonomy associated with the connection that transports a vector along a curve defined in a region of parameter space defined by a multiparameter family of Hermitian Hamiltonians. In general, this quantity is obtained by a path integral over some closed loop in parameter space for a quantum mechanical system undergoing an (*) adiabatic change. Barry Simon wrote an influential 1983 paper on this quantity. The most famous demonstration of the existence of this quantity are the interference fringes that result when a double-slit experiment is performed with a solenoidal coil which creates a vector potential that in turn induces this quantity. For 10 points, identify this quantity, a phase factor acquired by a particle in such experiments as the Aharonov-Bohm experiment.
This quantity is now used to explain the anomalous velocity that appears in Karplus and Luttinger's theory of the anomalous Hall effect.
Berry's phase [accept geometric phase]