Abstract
The dynamics of electric fields at a neutral or charged point in a one-component plasma is considered. The equilibrium joint probability density for electric-field values at two different times is defined, and several formally exact limits are described in some detail. The asymptotic short-time behavior for both neutral and charged-point cases is shown to be Gaussian with respect to the field differences, but with a half-width depending on their sum. In the strong-coupling limit, the joint probability density is dominated by weak fields (charged-point case), leading to a Gaussian distribution with time dependence entirely determined from the electric-field time-correlation function. The limit of large fields is shown to be determined by the time-dependent autocorrelation function for the density of ions around the field point; for the special case of fields at a neutral point, this result implies that the joint distribution at large fields is determined entirely by the dynamic structure factor. Finally, the full distribution (all field values and times) is studied in the weak-coupling limit.
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