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 f or a spin-1/2 quantum particle in the presence of a magnetic field rot ating on a cone with time. We find a commensurability condition to rea lize the cyclic evolution of both the system and Hamiltonian. In the a diabatic limit, this AA phase reduces to the geometric Berry phase. Mo re interestingly, such kind of geometric phase can manifest itself by producing a shift in the flux dependence of the conductance of a textu red mesoscopic ring connected to current leads.