Supercooled liquid regimes

In the supercooled liquid regime it is the structural relaxation which contributes the most to the friction and viscosity. Thus we can neglect the contribution from the transverse and longitudinal current. 

As discussed before, the viscoelastic model is known to provide a correct description of F(qz) in the intermediate density regime. Even in a supercooled liquid, it can provide correct short-time description, but fails in the long time, where the contribution from the hydrodynamic modes become important. 

In the supercooled liquid, the important part of the memory kernel is its long-time part, r (q, t). The recollision term contains the contribution from the hydrodynamic modes. As discussed by many authors [3, 30, 34], among all the hydrodynamic modes the density fluctuation is found to yield the main contribution to the memory kernel in the supercooled fluid regime. 

In the previous section we have discussed the relation between the time- and frequency-dependent friction and viscosity in the normal liquid regime. The study in this section is motivated by the recent experimental (see Refs. 80-87) and computer simulation studies [13,14, 88] of diffusion of a tagged particle in the supercooled liquid where the tagged particle has nearly the same size as the solvent molecules. These studies often find that although the fric-... 

---