Transverse Correlation and Transverse Mode in Simple Liquid

Properties of the transverse correlation and transverse modes in the dynamical region in a simple liquid are studied on the basis of the generalized Langevin equation. Under the assumption of Gaussian decay of the time correlation of the random forces, the molecular expressions for the transverse current correlation function and the transverse response function are obtained. Numerical calculations are made for the liquid argon at T =84.25 K. The analysis of spatial correlations shows that the local correlations in a liquid may conveniently be described by two parts, the radial and the angular parts. The damping of the correlation Δ ( k ) shows a very weak dependence on the wave number k . The dispersion relation of the transverse mode is obtained from the maximum of the correlation function. The analytical properties of the pole of the response function shows the possibility of the propagation of the transverse mode in the case where G / Δ 2 >0.294, G being related with the modulus of rigidity.