Two‐moment modelling of the dynamic longitudinal conductivity of strongly coupled Coulomb systems

Abstract

A dynamic longitudinal internal conductivity model, derived from the classical method of moments, is applied to the analysis of recent simulation data and reflectivity measurements of shock-compressed dense xenon plasmas. This model satisfies both the non-zero f −sum rule and the second non-zero sum rule, and reproduces the non-monotonicity of the conductivity of dense plasmas beyond the domain of applicability of the Drude-Lorentz model. The Drude-Lorentz model from the point of view of the theory of momentsThe classical model for the (internal) conductivity of dense plasmas and metals,is characterized by two static parameters, the static conductivity σ 0 = σ (ω = 0) = n e e 2 τm −1 = (4π) −1 ω 2 p τ and the relaxation time τ . Here n e is the number density of electrons in the system, −e and m are the electronic charge and mass, and ω p is the plasma frequency.In addition to direct measurements, the static conductivity value can be obtained as [1]Here σ ext (ω) is the external dynamic conductivity of the Coulomb system related to the internal conductivity through the well-known formula 1 [2]:Mathematically, the DL function, σ DL (z), is a simple Nevanlinna (response) function 2 with a single simple pole in the lower half-plane. In addition, the real part of σ DL (z) possesses a single finite frequency moment, which is known also as the f -sum rule:

Optical Properties of Model Moderately Coupled Plasmas

“…For further study of dynamic properties of cold plasmas in comparison with the simulation and experimental data see, [16]. Two-component plasmas (TCPs) constitute the simplest model that simulates the physical properties of real plasmas.…”

Investigation of dynamic properties of non-ideal one component plasmas by the method of moments

“…Certainly, the asymptotic behavior of the DSF observed in [9] Notice that alternative approaches like the QLCA or the continuedfraction method do not predict the damping of the plasmon modes. 45 …”

“…The Nevanlinna theorem [44], see also [45], states that there exists a oneto-one correspondence between the set of all solutions of the moment problem and the Nevanlinna functions , with the following additional property: In particular, among the functions (3.11) there is a unique function which, for a given , would yield:…”

“…For further study of dynamic properties of cold plasmas in comparison with the simulation and experimental data, see [45]. The model partial static structure factor was computed in [11], and more recently in [48], using the hypernetted-chain (HNC) approximation with the Deutsch effective potential.…”

“…Then, for the reconstruction of the spectra obtained in Ref. [45], the values of the moments and are to be calculated from the computed spectra. In particular, we must understand here that the plasma frequency computed from the simulations is an effective one, accounting for the total electronic density.…”