  We study the dynamics of the chiral phase transition in a linear quark-meson
$\sigma$ model using a novel approach based on semiclassical wave-particle
duality. The quarks are treated as test particles in a Monte-Carlo simulation
of elastic collisions and the coupling to the $\sigma$ meson, which is treated
as a classical field. The exchange of energy and momentum between particles and
fields is described in terms of appropriate Gaussian wave packets. It has been
demonstrated that energy-momentum conservation and the principle of detailed
balance are fulfilled, and that the dynamics leads to the correct equilibrium
limit. First schematic studies of the dynamics of matter produced in heavy-ion
collisions are presented.
