Starting from the linear sigma model with constituent quarks we derive the chiral fluid dynamics where hydrodynamic equations for the quark fluid are coupled to the equation of motion for the order-parameter field. In a static system at thermal equil
ibrium this model leads to a chiral phase transition which, depending on the choice of the quark-meson coupling constant, could be a crossover or a first order one. We investigate the stability of the chiral fluid in the static and expanding backgrounds 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 sigma-meson excitations. For large couplings 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 eta-space. In this case the growth rate of unstable modes is significantly reduced.
The constituent quark number scaling of elliptic flow is studied in a non-equilibrium hadronization and freeze-out model with rapid dynamical transition from ideal, deconfined and chirally symmetric Quark Gluon Plasma, to final non-interacting hadron
s. In this transition a Bag model of constituent quarks is considered, where the quarks gain constituent quark mass while the background Bag-field breaks up and vanishes. The constituent quarks then recombine into simplified hadron states, while chemical, thermal and flow equilibrium break down one after the other. In this scenario the resulting temperatures and flow velocities of baryons and mesons are different. Using a simplified few source model of the elliptic flow, we are able to reproduce the constituent quark number scaling, with assumptions on the details of the non-equilibrium processes.
The properties of compact stars made of massive bosons with a repulsive selfinteraction mediated by vector mesons are studied within the mean-field approximation and general relativity. We demonstrate that there exists a scaling property for the mass
-radius curve for arbitrary boson masses and interaction strengths which results in an universal mass-radius relation. The radius remains nearly constant for a wide range of compact star masses. The maximum stable mass and radius of boson stars are determined by the interaction strength and scale with the Landau mass and radius. Both, the maximum mass and the corresponding radius increase linearly with the interaction strength so that they can be radically different compared to the other families of boson stars where interactions are ignored.
