Dynamics and stability of chiral fluid

Starting from the linear sigma model with constituent quarks we derive hydrodynamic equations which are coupled to the order-parameter field, e.g. the chiral fluid dynamics. For a static system in thermal equilibrium this model leads to a chiral phase transition which, depending on the choice of the quark-meson coupling constant g, could be a crossover or a first order one. We investigate the stability of the chiral fluid in the static and expanding background by considering the evolution of perturbations with respect to the mean-field solution. In the static background the spectrum of plane-wave perturbations consists of two branches, one corresponding to the sound waves and another to the σ-meson excitations. For large g these two branches cross and the excitation spectrum acquires exponentially growing modes. The stability analysis is also done for the Bjorken-like background solution by explicitly solving the time-dependent differential equation for perturbations in the η space. In this case the growth rate of unstable modes is significantly reduced.