Structure formation during phase transitions in strongly interacting matter

A broad range of problems associated with phase transitions in systems characterized by the strong interaction between particles and with formation of structures is reviewed. A general phenomenological mean-field model is constructed describing phase transitions of the first and the second order to the homogeneous, $k_0=0$, and inhomogeneous, ${\overrightarrow{k}}_0\ne 0$ , states, the latter may occur even in case, when the interaction is translation-invariant. Due to fluctuations, the phase transition to the state, ${\overrightarrow{k}}_0\ne 0$, becomes the transition of the first order. Various specific features of the phase transitions to the state ${\overrightarrow{k}}_0\ne 0$ are considered such as the anisotropic spectrum of excitations, a possibility of the formation of various structures including running and standing waves, three-axis structures, the chiral waves, pasta mixed phases, etc. Next, a formal transition to hydrodynamical variables is performed. Then focus is made on description of the dynamics of the order parameter at the phase transitions to the states with ${\overrightarrow{k}}_0=0$ and ${\overrightarrow{k}}_0\ne 0$. In case of the phase transition to the inhomogeneous state the dynamics has specific features. Next the non-ideal hydrodynamical description of the phase transitions of the liquid–gas type in nuclear systems is performed. The ordinary Ginzburg–Landau model proves to be not applicable for description of an initial inertial stage of the seeds. Surface tension, viscosity and thermal conductivity are driving forces of phase transitions. Quasi-periodic structures are developed during the transitions. Next, the specific example of the pion condensation phase transition to the ${\overrightarrow{k}}_0\ne 0$ state in dense, cold or warm nuclear matter is considered and then the nuclear system at high temperature and small baryon chemical potential is studied, when baryons become completely blurred and light bosons, e.g., pions, may condense either in ${\overrightarrow{k}}_0=0$ or ${\overrightarrow{k}}_0\ne 0$ states. Then, for the scalar collective modes the phenomena of the Pomeranchuk instability and the Bose condensation in ${\overrightarrow{k}}_0=0$ or ${\overrightarrow{k}}_0\ne 0$ states are studied and a possibility of a metastable dilute nuclear state is discussed. Next, possibility of the condensation of Bose excitations in the ${\overrightarrow{k}}_0\ne 0$ state in the moving media is considered. Then Bose–Einstein condensation of pions with dynamically fixed number of particles is studied. Finally, specific purely non-equilibrium effects are demonstrated on an example of the sudden breaking up of the box filled by nucleons.