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This report addresses the moments, ${mathfrak{G}_n}left( {mathbf{q}} right) = int_{ - infty }^{ + infty } {{omega ^n}Sleft( {{mathbf{q}},omega } right)mathrm{d}omega },,n in mathbb{N},,n geq - 1$, of the quantum mechanical dynamic structure factor $Sleft( {{mathbf{q}},omega } right)$ for a one-component Coulomb plasma in thermodynamic equilibrium. The Fluctuation Dissipation Theorem relates these moments to integrals involving the imaginary part of the inverse longitudinal dielectric function, with the odd moments in particular being equivalent to the odd moments of the imaginary part of the inverse dielectric function. Application of the Generalized Plasmon Pole Approximation arXiv:1508.05606 [physics.plasm-ph] to a weakly-coupled non-degenerate plasma, leads to general formulae expressed in terms of polynomial functions. Explicit forms of these functions are given for $n leq 20$. These formulae are generalized to degenerate and partially degenerate plasmas, in small-$mathbf{q}$ (long-wavelength) regimes.
We have investigated the role of localized {it d} bands in the dynamical response of Au, on the basis of {it ab initio} pseudopotential calculations. The density-response function has been evaluated in the random-phase approximation. For small moment
The accurate description of electrons at extreme density and temperature is of paramount importance for, e.g., the understanding of astrophysical objects and inertial confinement fusion. In this context, the dynamic structure factor $S(mathbf{q},omeg
Frequency upconversion of an electromagnetic wave can occur in ionized plasma with decreasing electric permittivity and in split-ring resonator-structure metamaterials with decreasing magnetic permeability. We develop a general theory to describe the
We propose an algebraic method for proving estimates on moments of stochastic integrals. The method uses qualitative properties of roots of algebraic polynomials from certain general classes. As an application, we give a new proof of a variation of t
The $e-e$, $e-i$, $i-i$ and charge-charge static structure factors are calculated for alkali and Be$^{2+}$ plasmas using the method described by Gregori et al. in cite{bibGreg2006}. The dynamic structure factors for alkali plasmas are calculated usin