Geometric phases and anholonomy for a class of chaotic classical systems.

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this " classical parallel transport " is anholonomic — transport around a closed curve in parameter space does not bring a point in phase space back to itself — and is intimately related to the Robbins-Berry classical two-form.