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Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants

Ali Mostafazadeh
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Abstract

For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and the Floquet decompositions of the time-evolution operator is elucidated. In particular, a necessary condition for the occurrence of cyclic non-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic states are obtained for a magnetic dipole interacting with a precessing magnetic field.

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Ali Mostafazadeh. 1998-10-22. Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants. https://doi.org/10.1088/0305-4470%2F31%2F49%2F015

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