Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants
Abstract
Description
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
Plain LaTeX, 13 pages, accepted for publication in J. Phys. A: Math. Gen