Quasi-stationary states in the self-gravitating sheet model
  We study quasi-stationary states (QSS) resulting from violent relaxation in
the one-dimensional self-gravitating "sheet model", revisiting in particular
the question of the adequacy of the theory of Lynden-Bell (LB) to describe
them. For "waterbag" initial conditions characterized by a single phase space
density, the prediction of this theory is, in this model, a function of only
one parameter, which can conveniently be chosen to be the ratio of the energy
to that in the degenerate limit. Studying a class of such initial conditions in
which the shape of the initial waterbag is varied, we find that the LB
predictions are reasonably good always in the low energy region, while at
higher energies (i.e. in the non-degenerate limit) they are generally not even
qualitatively correct, although certain initial conditions can still be found
where they are as good as at low energy. We find notably that, in line with
what has been observed by Levin et al. in some other models, when LB theory
does not work the QSS are always characterized by the presence of a {\it
degenerate} core, which these authors explain as the result of dynamical
resonances. In short LB theory appears to be a good approximation only when
violent relaxation is sufficiently "gentle", and otherwise a degenerate
core-halo structure results.
