Figure 3

Dynamics and thermodynamics in the 3D Lennard-Jones fluid. (a–c) Dispersion relations \({\omega }_{L,T}(q)\) at temperatures \(T=17.2\), 20, and 23.2, respectively, calculated using the two-oscillator model (5) (orange circles), maxima of its transverse part \({C}_{T}(q,\omega )\) (black pentagons), and maxima of the longitudinal (LM) and transverse (TM) current spectra \({C}_{L,T}(q,\omega )\) (blue rhombs). The solid red lines are theoretical asymptotic curves \(\omega =cq\) given by Eq. (9). Grey zones show the regions \(q < 2\pi /L\) (L is the size of the considered system). (d) Temperature dependence of the specific heat \({C}_{V}(T)\). (e) Velocity autocorrelation functions (VAFs) at \(T=20\) and 23.2 (corresponding to the vicinity of \({C}_{V}=2\)). The inset presents a zoom of the region in the grey frame to highlight the change in the VAF with an increase in the temperature. (f) Temperature dependencies of q_g and q_* obtained using the two-oscillator model (orange circles) and maxima of its transverse part \({C}_{T}(q,\omega )\) (black pentagons), while triangles indicate confidence intervals. The blue region corresponds to the temperature range where the VAF becomes monotonic rather than oscillatory. The vertical blue dashed line is \(T\approx 21.1\) (at which \({C}_{V}=2\)), while the horizontal black dashed lines are the positions of the first pseudo-Brillouin zone boundary determined by different ways.