  We study exact time-evolving many-electron states of an open double
quantum-dot system with an interdot Coulomb interaction. A systematic
construction of the time-evolving states for arbitrary initial conditions is
proposed. For any initial states of one- and two-electron plane waves on the
electrical leads, we obtain exact solutions of the time-evolving scattering
states, which converge to known stationary scattering eigenstates in the
long-time limit. For any initial states of localized electrons on the quantum
dots, we find exact time-evolving states of a new type, which we refer to as
time-evolving resonant states. In contrast to stationary resonant states, whose
wave functions spatially diverge and not normalizable, the time-evolving
resonant states are normalizable since their wave functions are restricted to a
finite space interval due to causality. The exact time-evolving resonant states
enable us to calculate the time-dependence of the survival probability of
electrons on the quantum dots for the system with the linearized dispersions.
It decays exponentially in time on one side of an exponential point of
resonance energies while, on the other side, it oscillates during the decay as
a result of the interference of the two resonance energies.
