Non-Abelian Geometric Dephasing

Geometric dephasing in zero-field magnetic resonance

Geometric phases acquired randomly can give rise to coherence dephasing in nuclear spin systems, equivalent to spin relaxation. We calculate the form and extent of this geometric dephasing in a number of model systems involving the motion of Xe nuclei in shaped containers. The dephasing is calculated in two ways: first, using an analytical treatment of the diffusive motion of individual nuclei,...

Non-Abelian geometric phases in ground-state Josephson devices

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Noncyclic Geometric Phase and Its Non-Abelian Generalization

We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing definitions of the Abelian noncyclic geometric phase. We also discuss the adiabatic limit of the noncyclic geometric phase and compute the adiabatic non-Abelian ...

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

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-Ab...

Non-Abelian geometric effect in quantum adiabatic transitions.