  The connection between domain relaxations at individual scales and the
collective heterogeneous response in non-equilibrium systems is a topic of
profound interest in recent times. In a model sys- tem of constantly driven
oppositely charged binary colloidal suspension, we probe such relaxations as
the elongated lanes of likely charges interact with increasing field in the
orthogonal plane using Brownian Dynamics simulations. We show that the system
undergoes a structural and dynamical cross-over: from an initial fast-relaxing
homogeneous phase to a heterogeneous lane phase following a slow relaxation via
an intermediate phase with mixed relaxation. Our observations also affirm the
coexistence of multiple time and length scales in this phase. Unlike glasses,
these time and length scales are not separated by orders of magnitude, they are
comparable in magnitudes. Using a phenomenological model, we, further,
reinforce that these competing relaxations are a manifesta- tion of
heterogeneity in diffusion which is rather generic in systems with such
competing relaxations.
