In the framework of the linear sigma model, we study the time evolution of a
system of classical σ and pion fields coupled to quarks. For this
purpose we solve numerically the classical transport equation for relativistic
quarks coupled to the nonlinear Klein-Gordon equations for the meson fields. We
examine evolution starting from variety of initial conditions corresponding to
spherical droplets of hot quark matter, which might mimic the behaviour of a
quark plasma produced in high-energy nucleus-nucleus collisions. For large
droplets we find a strong amplification of the pion field that oscillates in
time. This leads to a coherent production of pions with a particular isospin
and so would have similar observable effects to a disoriented chiral condensate
which various authors have suggested might be a signal of the chiral phase
transition. The mechanism for amplification of the pion field found here does
not rely on this phase transition and is better thought of as a "pion laser"
which is driven by large oscillations of the σ field.Comment: 12 TeX pages + 20 postscript figures, psfig styl