Non-hydrodynamic modes in viscoelastic behaviour of simple fluids

We discuss the role of non-hydrodynamic processes in viscoelastic transition in pure liquids. In particular, using both analytical results and molecular dynamics simulations, we clarify the effect of the shear stress relaxation on the transverse dynamics. We use as an example the Lennard-Jones fluids. We analyse the frequency dependence of the shear modulus and its connection to the non-hydrodynamic shear relaxation mode. The analysis of the relaxation times of the non-hydrodynamic modes in longitudinal and transverse dynamics makes evidence that the emergence of the non-hydrodynamic transverse excitations outside the propagation gap is not directly connected to the onset of the positive sound dispersion.