Quasi-solid state microscopic dynamics in equilibrium classical liquids: Self-consistent 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 $C_{\mathrm{T}}(k,\omega)$ of the transverse particle current realized in a range of wave numbers $k$. In the domain of microscopic spatial scales comparable to the action range 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 the dispersion law for transverse (shear) acoustic waves and also relations for the kinematic shear viscosity $\nu$, the transverse speed of sound $v^{({\mathrm{T}})}$, and the corresponding sound damping coefficient $\Gamma^{({\mathrm{T}})}$. We compare the theoretical results with the results of atomistic dynamics simulations of liquid lithium near the melting point.