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 $k_0=0$ and $\vec{k}_0\neq 0$ states. Due to fluctuations, the phase transition to the state $\vec{k}_0\neq 0$ is the transition of the first order. Various specific features of the phase transitions to the state $\vec{k}_0\neq 0$ 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, chiral waves, pasta phases, etc. 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 $\vec{k}_0= 0$ and $\vec{k}_0\neq 0$. Next the non-ideal hydrodynamical description of the phase transitions of the liquid-gas type in nuclear systems is performed. Quasiperiodic structures are developed. Next, pion condensation phase transition to the $\vec{k}_0\neq 0$ state in dense, cold or warm nuclear matter is considered and then the high temperature -- small baryon chemical potential system is studied, when baryons become completely blurred and light bosons, e.g., pions, may condense either in $\vec{k}_0= 0$ or $\vec{k}_0\neq 0$ states. Then, for scalar collective modes phenomena of the Pomeranchuk instability and the Bose condensation in $\vec{k}_0= 0$ or $\vec{k}_0\neq 0$ states are studied. Next, possibility of the condensation of Bose excitations in the $\vec{k}_0\neq 0$ state in moving media is considered. Then Bose-Einstein condensation of pions at dynamically fixed number of particles is studied and specific non-equilibrium effects are demonstrated on an example.