Nonadiabatic Noncyclic Geometric Phase and Ensemble Average Spectrum of Conductance in Disordered Mesoscopic Rings with Spin-Orbit Coupling

We generalize Yang's theory from the $\mathrm{U}\left(1\right)$ gauge field to the non-Abelian $\mathrm{U}\left(1\right)\times \mathrm{SU}(2{)}_{\mathrm{spin}}$ gauge field. Based on this generalization and taking into account the geometric Pancharatnam phase as well as an effective Aharonov-Bohm (AB) phase in nonadiabatic noncyclic transport, we calculate the ensemble average Fourier spectrum of the conductance in disordered mesoscopic rings connected to two leads. Our theory can explain the experimental results reported by Morpurgo et al. [Phys. Rev. Lett. 80, 1050 (1998)] more satisfactorily. We indicate that the observed splitting stems from the nonadiabatic noncyclic Pancharatnam phase and the effective AB phase, both being dependent on spin-orbit coupling.