Exotic collective dynamics in molten Carbon

Collective longitudinal and transverse propagating modes in molten Carbon at $T=5500$~K and pressure range $10$-$40$ GPa are reported from {\it ab initio} based as well as machine learned molecular dynamics. A striking exotic feature in collective dynamics is the two-peak shape of the current spectral functions of the single-component liquid, which makes evidence of a second branch of longitudinal propagating modes in the wave number range $k>1$\AA$^{-1}$. It is shown that time correlation functions reflecting the out-of-phase motion of particles and their cages of nearest neighbors results in the same frequencies of the exotic low-frequency branch of vibrations. A theoretical framework of generalized collective modes is applied to recover the time dependence of density-density, imaginary part of susceptibility and longitudinal current-current correlations.