Aharonov-Anandan phase in a textured mesoscopic ring connected to current leads at extremely low temperatures

We calculate exactly a kind of Aharonov-Anandan (AA) geometric phase for a spin-1/2 quantum particle in the presence of a magnetic field rotating on a cone with time. We find a commensurability condition to realize the cyclic evolution of both the system and Hamiltonian. In the adiabatic limit, this AA phase reduces to the geometric Berry phase. More interestingly, such kind of geometric phase can manifest itself by producing a shift in the flux dependence of the conductance of a textured mesoscopic ring connected to current leads.