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Adiabatic Berry Phase and Hannay Angle for Open Paths

Arun Kumar Pati

arXiv:quant-ph/9804057Annals of PhysicsNov 1, 199836 citations

Geometric Phases for Classical and Quantum Dynamics: Hannay Angle and Berry Phase for Loops on a Torus

Subir Ghosh

arXiv:1905.03491International Journal of Theoretical PhysicsJun 7, 20192 citations

Berry phase and Hannay’s angle in the Born–Oppenheimer hybrid systems

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

Annals of PhysicsAug 11, 20136 citations

27p-ED-1 Berry's Phase and Fractional Quantization of Adiabatic Motion

晋司飯田, 比呂志倉辻

年会講演予稿集Mar 27, 19870 citations

Classical adiabatic holonomy in a Grassmannian system

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.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.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsApr 15, 198731 citations

Vanishing Theorems for Hannay Angle and Berry Phase

Minoru Hirayama, Toshihiko TAJIMA

The classical Hannay angle and the quantal Berry phase are discussed for systems involving neither dimensionless adiabatic parameters nor vector potentials. Both of them are shown to vanish generally in a flat space. They are also shown to vanish in any n -dimensional curved space which can be embedded in an ( n + 1)-dimensional Euclidean space.

Progress of Theoretical PhysicsApr 1, 19880 citations

Hannay's Angle and Berry's Phase in the Classical Adiabatic Motion of Charged Particlesa

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