Anholonomy, Hannay Angle and Berry Phase for Non-Bounding Cycles on a Torus

Subir Ghosh

Arun Kumar Pati

Robert G. Littlejohn

G. Giavarini, E. Gozzi, Daniel Rohrlich +1 more

In this paper we study the interplay between the classical and quantum anholonomy effects (Hannay's angle and Berry's phase). When a quantum system with a finite number of energy levels has a Berry phase, it also has a nonzero Hannay angle. We show how systems with infinitely many levels can evade this correspondence, and find some necessary conditions for a system with a Berry phase to have no Hannay angle.

Luiz Agostinho Ferreira, Abraham Hirsz Zimerman, J. F. Gomes

Nilanjana Datta, Gautam Kumar Ghosh

We study classical and quantum anholonomy for nonlinear oscillators which support linear or quadratic spectra. The validity of the semiclassical relation between Berry's phase and Hannay's angle is investigated.