Journal of Statistical Physics, Vol. 41, Nos. 5/6, 1985, p. 941-974.
Sum rules describing perfect screening at equilibrium in a classical plasma are
extended to the time-displaced structure function of an inhomogeneous one-
component plasma. We find that there are long-wavelength modes which
oscillate undamped with a single frequency 03, 032 being an angular average of
the squared plasma frequency at infinity. Our results are derived heuristically,
allowing also for quantum effects, from linear response theory, and rigorously
from the classical BBGKY hierarchy under some reasonable assumptions on the
spatial decay of correlations. Special cases are investigated, in particular
plasmas bounded by walls of varied shapes.