The interplay between structure and dynamics in non-equilibrium steady-state is far from understood. We address this interplay by tracking Brownian Dynamics trajectories of particles in a binary colloid of opposite charges in an external electric field, undergoing cross-over from homogeneous to lane state, a prototype of heterogeneous structure formation in non-equilibrium systems. We show that the length scale of structural correlations controls heterogeneity in diffusion and consequent anomalous dynamic responses, like the exponential tail in probability distributions of particle displacements and stretched exponential structural relaxation. We generalise our observations using equations for steady state density which may aid to understand microscopic basis of heterogeneous diffusion in condensed matter systems. The dynamic response depicts how disturbance in any thermodynamic quantity in a system relaxes with time via particle motion [1,2]. This forms the microscopic basis of transport processes [1][2][3][4], like diffusion in liquids. In general particle dynamics depends on the structure of the system. Nonequilibrium systems often show emergence of structural heterogeneity in steady states, known as pattern formation [5] relevant in areas ranging from material science to biological systems [3,4]. The particle dynamics in such systems is nontrivial due to drive [6][7][8][9]. Despite large number of studies [3][4][5][6][7][8][9], the connections between dynamics and structure, and consequently, the transport processes are not well understood for non-equilibrium situations. This motivates us to explore dynamic responses and relate them to the underlying structural morphology in non-equilibrium steady states.Colloids are ideal model system to realize condensed matter properties both in and out of equilibrium [3,4,6,7]. Variety of structures can be induced in colloids by external perturbations [3,4,[6][7][8][9]. Moreover, the particles are big enough for optical imaging and are slow so that the particle motions can be followed [1][2][3][4][6][7][8][9]. Several experiments and theoretical works show that in an external uniform electric field of large strength drives a binary mixture of oppositely charged colloids to form heterogeneous structure in the steady state with lanes of dynamically locked-in like-charged particles, while the mixture is homogeneous at low field [3,4,[6][7][8][9][10][11][12][13][14][15][16].We consider steady states of binary charged colloid in electric field. The steady state structural correlations are given by the pair correlation functions(PCF) [1] which are probability distributions of particle separations at a given time. We study how density changes relax via microscopic motion in * Electronic address: Email:sumand@bose.res.in † Electronic address: Email:jaydeb@bose.res.in different steady state structures of binary charged colloid in electric field. The density relaxation, also known as the van Hove function (vHf) [17], is measurable from scattering experiments and routinely used in ...

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In a model system of oppositely charged colloids we study via Brownian dynamics simulation the dynamical response as the system approaches steady states upon application of a constant electric field. The system is known to form patterns of like charges in the transverse plane to the field that are elongated along the field as lanes. We show that an increase in structural heterogeneity leads to non-Gaussian tails in the probability distribution of particle displacements [self van Hove functions (self-vHfs)]. The self-diffusion coefficient depends upon the time of the observations and consequently indicates aging in the system. However, the anomalies in the self-vHfs and diffusion do not appear during the melting of the structures.

Dynamical heterogeneity (DH) in non-equilibrium systems is a topic of profound interest yet an open question. In a model system of constantly driven oppositely charged binary colloidal suspension, we explore DH in a model lane-forming system using BD simulations. We show that the system undergoes structural and dynamical cross-over using spatio-temporal correlation functions. For small field, the structural relaxation is homogeneous while it is heterogeneous for sufficiently high field. In order to explore the heterogeneity, we track and tag the particles to compute partial structures that relax at different rates, in which heterogeneity has its maximum in the intermediate state.

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