Adiabatic Berry Phase and Hannay Angle for Open Paths

Robert G. Littlejohn

H. D. Liu, X. X. Yi, Libin Fu

Subir Ghosh

Gautam Kumar Ghosh, Binayak Dutta-Roy

The analysis provided by Berry of the extra phase acquired by a system undergoing adiabatic excursion in a closed path in parameter space is extended in this paper to the case of nonstationary states. It is shown that, for certain integrable dynamical systems, wave packets exist which under continuation in parameter space behave in a manner that can be understood entirely in classical terms, thus providing a connection between the quantum adiabatic phase and the classical Hannay angle shifts.

David H. Vanderbilt

E. Gozzi, William D. Thacker

The ``geometrical phase factor,'' found by Berry in his study of the quantum adiabatic theorem, has a classical analogue discovered recently by Hannay and Berry himself. This classical analogue consists of an extra angle swept by the system in its classical evolution during an adiabatic excursion. As in Berry's phase, Hannay's angle reflects a nontrivial holonomy of the system and it has a purely geometric character. In this paper we calculate Hannay's angles for the classical Grassmannian system associated to a quantum spin in a magnetic field. We also show their close relation to the corresponding quantum-mechanical phase of Berry for the same system.