  The nonequilibrium real-time dynamics of electron coherence is explored in
the quantum transport through the double-dot Aharonov-Bohm interferometers. We
solve the exact master equation to find the exact quantum state of the device,
from which the changes of the electron coherence through the magnetic flux in
the nonequilibrium transport processes is obtained explicitly. We find that the
relative phase between the two charge states of the double dot localizes to
$\frac{\pi}{2}$ or $-\frac{\pi}{2}$ for all different magnetic flux. This
nontrivial phase localization process can be manifested in the measurable
occupation numbers.
