Frequency and Wavevector Dependence of the Atomic Level Stress-Stress Correlation Function in a Model Supercooled Liquid*

Temporal and spatial correlations among the local atomic level shear stresses were studied for a model liquid iron by molecular dynamics simulation [PRL 106,115703]. Integration over time and space of the shear stress correlation function $F(r,t)$ yields viscosity via Green-Kubo relation. The stress correlation function in time and space $F(r,t)$ was Fourier transformed to study the dependence on frequency, $E$, and wave vector, $Q$. The results, $F(Q,E)$, showed damped shear stress waves propagating in the liquid for small $Q$ at high and low temperatures. We also observed additional diffuse feature that appears as temperature is reduced below crossover temperature of potential energy landscape at relatively low frequencies at small $Q$. We suggest that this additional feature might be related to dynamic heterogeneity and boson peaks. We also discuss a relation between the time-scale of the stress-stress correlation function and the alpha-relaxation time of the intermediate self-scattering function $S(Q,E)$.