Two-moment modelling of the dynamic longitudinal conductivity of strongly coupled Coulomb systems D. Ballester and I.M. Tkachenko * Department of Applied Mathematics, Polytechnic University of Valencia, 46022 Valencia, Spain Received 25 March 2005, accepted 25 April 2005 Published online 13 June 2005 Key words Dynamic conductivity, dielectric properties, strongly coupled Coulomb systems. PACS 52.25.Mq, 71.45.Gm, 52.27.Gr, 71.10.Ca 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 plas- mas. 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. c  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 The Drude-Lorentz model from the point of view of the theory of moments The classical model for the (internal) conductivity of dense plasmas and metals, σ DL (ω)= σ 0 1 − iωτ , (1) 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] σ 0 = lim ω↓0 Reσ ext (ω) ω 2 . (2) 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]: σ(ω)= σ ext (ω) 1 − 4πi ω σ ext (ω) . (3) 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: µ 0 =  ∞ -∞ Reσ DL (ω) dω = ω 2 p 4 . (4) ∗ Corresponding author: e-mail: imtk@mat.upv.es, Phone: +34 963 876 646 Fax: +34 963 877 179 1 Here we consider the long-wavelength dynamic properties of plasmas. 2 A function F (z) belongs to the class of Nevannlina functions if F (z) is analytic in Imz> 0 and ImF (z) ≥ 0 in Imz> 0. c  2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Contrib. Plasma Phys. 45, No. 3-4, 293 – 299 (2005) / DOI 10.1002/ctpp.200510033