Heterogeneous Dynamical Relaxations in a Lane Forming Liquid

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.