Quasi-solid state microscopic dynamics in equilibrium classical liquids: Self-consisnent relaxation theory

In the framework of the concept of time correlation functions, we develop a self-consistent relaxation theory of the transverse collective particle dynamics in liquids. The theory agrees with well-known results in both the short-wave (free particle dynamics) and the long-wave (hydrodynamic) limits. We obtain a general expression for the spectral density~$C_T(k,\omega)$ of transverse particle current realized in the range of wave numbers $k$. In domain of microscopic spatial scales comparable to action scale of effective forces of interparticle interaction, the theory reproduces a transition from a regime with typical equilibrium liquid dynamics to a regime with collective particle dynamics where properties similar to solid-state properties appear: effective shear stiffness and transverse (shear) acoustic waves. In the framework of the corresponding approximations, we obtain expressions for the spectral density of transverse particle current for all characteristic regimes in equilibrium collective dynamics. We obtain expressions for dispersion law for transverse (shear) acoustic waves and also relations for the kinematic shear viscosity $\nu$, the transverse speed of sound $v^{(T)}$, and the corresponding sound damping coefficient $\Gamma^{(T)}$. We compare the theoretical results with the results of atomic dynamics simulations of liquid lithium near the melting point.