  We calculate the oscillations of the DC conductance across a mesoscopic ring,
simultaneously tuned by applied magnetic and electric fields orthogonal to the
ring. The oscillations depend on the Aharonov-Bohm flux and of the spin-orbit
coupling. They result from mixing of the dynamical phase, including the Zeeman
spin splitting, and of geometric phases. By changing the applied fields, the
geometric phase contribution to the conductance oscillations can be tuned from
the adiabatic (Berry) to the nonadiabatic (Ahronov-Anandan) regime. To model a
realistic device, we also include nonzero backscattering at the connection
between ring and contacts, and a random phase for electron wavefunction,
accounting for dephasing due to disorder.
