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Dynamical properties of uniform electron fluids (jellium model) are studiedwithin a novel non-perturbative approach consisting in the combination of theself-consistent version of the method of moments (SCMM) involving up to ninesum rules and other exact relations, the two-parameter Shannon informationentropy maximization procedure, and the ab initio path integral Monte Carlo(PIMC) simulations of the imaginary-time intermediate scattering function.  The explicit dependence of the electronic dynamic structure factor (DSF) ontemperature and density is studied in a broad realm of variation of thedimensionless parameters ($2\leq r_s\leq 36$ and $1\leq \theta \leq 8$). Whenthe coupling is strong ($r_s\geq 16$) we clearly observe a bi-modal structureof the excitation spectrum with a lower-energy mode possessing a wellpronounced roton-like feature ($\theta \leq 2$) and an additional high-energybranch within the roton region which evolves into the strongly overdampedhigh-frequency shoulder when the coupling decreases ($r_s\leq 10$). We are notaware of any reconstruction of the DSF at these conditions with the effects ofdynamical correlations, included here via the intermediate scattering and thedynamical Nevanlinna parameter functions. The standard static-local-fieldapproach fails to reproduce this effect. The reliability of our method isconfirmed by a detailed comparison with the recent ab initiodynamic-local-field approach by Dornheim et al. [Phys.Rev.Lett. 121, 255001(2018)] available for high/moderate densities ($r_s\leq 10$). Moreover, withinthe SCMM we are able to construct the modes dispersion equation in a closedanalytical form and find the decrements (lifetimes) of the quasiparticleexcitations explicitly. The physical nature of the revealed modes is discussed.Mathematical details of the method are complemented in the SupplementaryMaterial.

physical review. b./physical review. b

Analysis of dynamical effects in the uniform electron liquids with the  self-consistent method of moments complemented by the Shannon information  entropy and the path-integral Monte-Carlo simulations