Non-adiabatic non-abelian geometric phase

Jing Yang, Junqi Ge

Anatoly I. Ivanov, V.V. Berezuk

Ali Mostafazadeh

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 noncyclic geometric phase for a spin-1 magnetic (or electric) quadrupole interacting with a precessing magnetic (electric) field.

刘继兵, 李家华, 吕新友 +1 more

Ohjong Kwon, Chang-Jun Ahn, Y. D. Kim

We quantitatively formulate the nonadiabatic non-Abelian geometric phase by generalizing the Lewis invariant method to a degenerate case, which is reduced to Wilczek and Zee's [Phys. Rev. Lett. 52, 2111 (1984)] non-Abelian geometric phase in the adiabatic limit. We also derive the effective propagator accommodating the nonadiabatic non-Abelian geometric phase and the semiclassical quantization rule in the adiabatic limit.

A. A. Abdumalikov, J. M. Fink, Kristinn Júlíusson +4 more