Fig. 3. Behaviour of velocity correlation functions.

a Velocity correlations in Fourier space for the soft disk model for different τ at T_eff = 0.005 in the glassy phase and b: for changing T_eff at τ =  20. Dots correspond to the simulated velocity correlation function, solid lines are the results from the normal mode expansion Eq. (6), and the dashed lines are the continuum elasticity predictions Eq. (10). c Fourier velocity correlations for the SPV model, together with analytical prediction. d Mean-square velocity as a function of ξ_T∕a for both soft disks and the SPV model and analytical predictions (solid lines). All correlation functions have been normalized by $v_0^2=2T_{\mathrm{eff}}∕\tau$, and there are no fit parameters in the predictions.