Berry phase in homogeneous Kähler manifolds with linear Hamiltonians

Details Berry phase in homogeneous Kähler manifolds with linear Hamiltonians Berry phase in homogeneous Kähler manifolds with linear Hamiltonians

2001-11-13

arxiv.org/abs/math-ph/0111022v1

J.Math.Phys. 42, No.11 (2001) 5130-5142

Physics

Mathematical Physics

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We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of {\em classical} objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states.

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