Apparent Violation of the Fluctuation-Dissipation Theorem due to Dynamic Heterogeneity in a Model Glass-Forming Liquid

Here we study the relation between the mobility and the translational diffusion in supercooled two-dimensional polydisperse colloidal liquids, using numerical simulations. We find an apparent violation of the Einstein-Smoluchowski (ES) relation D=k_BTμ (D: diffusion constant; μ: mobility; k_B; Boltzmann’s constant; T: temperature). The violation is a direct consequence of the fact that it is difficult for a driven particle to enter a jammed region with high order due to its yield stress. The degree of this apparent ES violation is controlled solely by the characteristic size of slow jammed regions, ξ. Our finding implies that the characteristic time of this problem is not the structural relaxation time τ_α but the lifetime of dynamic heterogeneity, τ_ξ. A supercooled liquid can be regarded to be ergodic only over τ_ξ, which may be the slowest intrinsic time scale of the system.