Dynamic length scales and feedback from long-time structural relaxation in a simple liquid

Liquid can sustain shear waves up to a minimum wavenumber, indicating solid-like behaviour over short length scales. With the increase of density this critical wavenumber decreases, indicating a growth of a dynamic length scale. The speed of the propagating shear waves goes to zero approaching a critical wavenumber. The maximum wavelength shows an initial enhancement approaching the mode-coupling transition and finally grows at a slower rate as the sharp transition is cut off. The growth of this dynamic length scale in the supercooled regime is studied using the transverse correlation function and by computing the feedback effects of dynamic correlation in an extended mode-coupling model where the structure factor of the liquid is used as an input