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

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.

Plain LaTeX, 13 pages, accepted for publication in J. Phys. A: Math. Gen

References in corpus (1)

• Extending the quantal adiabatic theorem: Geometry of noncyclic motion

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