# Computer Simulation of Collective Modes and Transport Coefficients of Strongly Coupled Plasmas

• Jean-Pierre Hansen
Chapter
Part of the NATO Advanced Study Institutes Series book series (volume 36)

## Abstract

Consider a periodic system of N point ions of charge Ze and mass M in a rigid, neutralizing uniform background. For a given configuration $$\mathop r\limits^{ \to N} = \left( {{{\mathop r\limits^ \to }_1},\mathop {{r_2}}\limits^ \to ...,{{\mathop r\limits^ \to }_{\rm N}}} \right)$$ of the ions, the total potential energy of the system is:
$${V_N} = \frac{1}{{2v}}{\sum\limits_{k \ne \circ } {\frac{{4\pi \left( {Ze} \right)}}{{{k^2}}}} ^2}\left( {\rho _k^ \to \rho _{ - k}^ \to - {\rm N}} \right)$$
(1.1)
where:
$$\rho _k^ \to = \sum\limits_{i = 1}^N {_ei\mathop k\limits^ \to }.{\mathop r\limits^ \to _i}$$
(1.2)
Excess thermodynamic properties, and more generally, all reduced(dimensionless) equilibrium properties depend on the single dimensionless variable:
$$\Gamma = {\frac{{\left( {Ze} \right)}}{{a{k_B}T}}^2}$$
(1.3)
where a = (3/4πρ)1/3, ρ = N/V. We shall frequently use reduced distance x = r/a and wave numbers q = k/a. To describe dynamical (or time-dependent) properties we introduce an additional time variable t which we express in a “natural” unit, equal to the inverse of the plasma frequency:
$${\omega _p} = {\sqrt {\frac{{4\pi \left( {Ze} \right)}}{M}} ^2}$$
(1.4)

### Keywords

Entropy Autocorrelation Compressibility

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