2 4 Ja n 20 02 Transport Coefficients of the Yukawa One Component Plasma

We present equilibrium molecular-dynamics computations of the thermal conductivity and the two viscosities of the Yukawa one-component plasma. The simulations were performed within periodic boundary conditions and Ewald sums were implemented for the potentials, the forces, and for all the currents which enter the Kubo formulas. For large values of the screening parameter, our estimates of the shear viscosity and the thermal conductivity are in good agreement with the predictions of the Chapman-Enskog theory. 52.27.Gr, 52.25.Fi, 52.27.Lw Typeset using REVTEX ∗e-mail: [email protected] †e-mail: [email protected] 1 Recently, many numerical studies of the Yukawa one-component plasma (YOCP) i.e. a system made of N identical classical point particles of charge q and mass m which are embedded in a uniform neutralizing background of volume V and which interact via Yukawa pair potentials v(r) = q exp(−αr)/r have been performed in view of applications for a broad variety of systems, including dusty plasmas, inertial confinement fusion dense plasmas, jovian planets, brown and white dwarfs, etc. The excess free energy f as well as all the thermodynamic properties of the YOCP depend only upon two parameters, namely the coupling parameter Γ = βq/a, where β = 1/kT is the inverse temperature and a the ionic radius (4πρa/3 = 1, ρ = N/V number density), and the reduced screening parameter α = αa. In the special case where α = 0 one recovers the well-known one-component plasma (OCP) [1]. The other limiting case α → ∞ is that of a dilute gase for which simple approximate schemes can safely be used. The thermodynamic and structural properties of the YOCP have been thoroughly studied by means of equilibrium molecular dynamics (EMD) simulations within periodic boundary conditions (PBC) [2,3] and by Monte Carlo simulations on the hypersphere [4]. Reliable estimates of the free energy f(Γ, α) are thus available in a wide range of (Γ, α) [2–4]. By contrast, very little is known about the dynamical properties of the model. In view of hydrodynamical simulations, precise estimates of the transport coefficients of the YOCP are clearly wanted. Attempts to compute the shear viscosity η by means of non-equilibrium molecular dynamics (NEMD) simulations were discussed recently in the literature [5]. In this letter we present (EMD) computations not only of η, but also of the bulk viscosity ξ and the thermal conductivity λ. It turns out that our results for η differ significantly from those of ref. [5], a puzzling point which will be discussed further on. As it is well known, the three transport coefficients η, ξ, and λ are given by the Kubo formulas [6–8] : η = β V ∫ ∞ 0 〈σxy(t)σxy(0)〉 dt , (1a)