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28 March 2024
 
  » arxiv » quant-ph/0011120

 Article overview


Berry's phase for compact Lie groups
E. Strahov ;
Date 30 Nov 2000
Subject quant-ph
AbstractThe 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 Kähler manifold its fundamental Kähler 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.
Source arXiv, quant-ph/0011120
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