Adiabatic Berry phase and Hannay angle for open paths

Abstract

We obtain the adiabatic Berry phase by defining a generalised gauge potential whose line integral gives the phase holonomy for arbitrary evolutions of parameters. Keeping in mind that for classical integrable systems it is hardly clear how to obtain the open-path Hannay angle, we establish a connection between the open-path Berry phase and Hannay angle by using the parametrised coherent state approach. Using the semiclassical wavefunction we analyse the open-path Berry phase and obtain the open-path Hannay angle. Further, by expressing the adiabatic Berry phase in terms of the commutator of instantaneous projectors with its differential and using Wigner representation of operators we obtain the Poisson bracket between the distribution function and its differential. This enables us to talk about the classical limit of the phase holonomy which yields the angle holonomy for open paths. An operational definition of the Hannay angle is provided based on the idea of the classical limit of the quantum mechanical inner product. A probable application of the open-path Berry phase and Hannay angle to the wave-packet revival phenomena is also pointed out.