Berry's phase for compact Lie groups

Details Berry's phase for compact Lie groups Berry's phase for compact Lie groups

2000-11-30

arxiv.org/abs/quant-ph/0011120v1

Physics

Quantum Physics

24 pages, no figures

Scientific paper

10.1063/1.1358879

The Lie group adiabatic evolution determined by a Lie algebra parameter dependent Hamiltonian is considered. It is demonstrated that in the case when the parameter space of the Hamiltonian is a homogeneous K\"ahler manifold its fundamental K\"ahler potentials completely determine Berry geometrical phase factor. Explicit expressions for Berry vector potentials (Berry connections) and Berry curvatures are obtained using the complex parametrization of the Hamiltonian parameter space. A general approach is exemplified by the Lie algebra Hamiltonians corresponding to SU(2) and SU(3) evolution groups.

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