Evolution of Quasiperiodic Structures in a Non-Ideal Hydrodynamic Description of Phase Transitions

D N Voskresensky

doi:10.3390/universe6030042

D N Voskresensky

Open Access

https://doi.org/10.3390/universe6030042

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Abstract

Various phase transitions could have taken place in the early universe, and may occur in the course of heavy-ion collisions and supernova explosions, in proto-neutron stars, in cold compact stars, and in the condensed matter at terrestrial conditions. Most generally, the dynamics of the density and temperature at first- and second-order phase transitions can be described with the help of the equations of non-ideal hydrodynamics. In the given work, some novel solutions are found describing the evolution of quasiperiodic structures that are formed in the course of the phase transitions. Although this consideration is very general, particular examples of quark-hadron and nuclear liquid-gas first-order phase transitions to the uniform k 0 = 0 state and of a pion-condensate second-order phase transition to a non-uniform k 0 ≠ 0 state in dense baryon matter are considered.

Highlights

Cosmological observations of the two last decades [1] have supplied us with some extraordinary results and puzzles
Important is the fact that the universe undergoes an accelerated expansion and the fact that only 5% of its mass is contained in baryons, 26% is in dark matter, and the remaining part is in dark energy
The standard model does not account for the presence of the dark matter with which additional cosmic phase transitions may be associated during the cooling of the expanding universe to its present temperature T ' 2.7 K, cf. [10]

Summary

Introduction

Cosmological observations of the two last decades [1] have supplied us with some extraordinary results and puzzles. The quark-hadron, pion, kaon, and charged rho-meson condensate phase transitions may occur during the iso-entropical falling of the baryon-rich matter in supernova explosions [11], in proto-neutron stars, and in cold compact stars, cf [12] In some models, these phase transitions are considered first-order phase transitions leading to mixed phases in dense matter. When the adiabatic trajectory s = const enters the region of the first-order phase transition (the region below the solid curve in Figure 2), the approximation of the constant entropy fails, and a further description of the dynamics of the system requires a solution of non-ideal hydrodynamical equations [54,55,56]. The description of the dynamics of the second-order phase transition requires a solution of non-ideal hydrodynamical equations in the case where the density and the temperature (or entropy) can be considered appropriate order parameters.

Typical Time Scales

Stationary Solutions

Dynamics of Fluctuations in Unstable Region

The Growth of Fluctuations of Arbitrary Amplitude: A Nonlinear Regime

Findings

Conclusions