  Response of the electronic current through an Aharonov-Bohm ring after a
two-level-system is switched on is calculated perturbatively by use of
non-equilibrium Green function. In the ballistic case the amplitude of the
Aharonov-Bohm oscillation is shown to decay to a new equilibrium value due to
scattering into other electronic states. Relaxation of Altshuler-Aronov-Spivak
oscillation in diffusive case due to dephasing effect is also calculated. The
time scale of the relaxation is determined by characteristic relaxation times
of the system and the splitting of two-level-system. Oscillation phases are not
affected. Future experimental studies of current response may give us direct
information on characteristic times of mesoscopic systems.
