Topological phase transition

Here w is a weighting factor. Asr (s) is the absorption factor (in this case for symmetrical absorption), Hz (5) and In consider the non-ideal character of the two-phase topology (cf. p. 124, Fig. 8.10) by consideration of a smooth phase transition zone and density fluctuations inside the phases. 

Abstract. We review the recent development of quantum dynamics for nonequilibrium phase transitions. To describe the detailed dynamical processes of nonequilibrium phase transitions, the Liouville-von Neumann method is applied to quenched second order phase transitions. Domain growth and topological defect formation is discussed in the second order phase transitions. Thermofield dynamics is extended to nonequilibrium phase transitions. Finally, we discuss the physical implications of nonequilibrium processes such as decoherence of order parameter and thermalization. 

Keywords Nonequilibrium phase transitions, Liouville-von Neumann approach, domain growth, topological defect formation. 

Now we study the effects of the dynamical processes of nonequilibrium phase transitions on domain growth and topological defects. The quench models describe such nonequilibrium processes, which can be... 

Lipid assemblies of the lamellar type, such as lipid bilayers, can feature a true phase transition in which the topology does not change. Upon cooling, the bilayer goes from the fluid phase to the gel phase. In the fluid phase, the acyl chains are disordered, in the sense that there is enough free volume around the chains to allow for chain conformation variations. In the gel phase, the acyl chains are more densely packed and believed to be ordered in an all-trans (straight) configuration. For very pure systems, at temperatures below this sharp gel-to-liquid phase transition, there are several other states and distinct transitions detectable (pre-transition, ripple phase, etc.). These phases will not be reviewed here. In biomembranes, many type of lipids (and other molecules) occur, and it is known that for this reason the gel-to-liquid phase transition is... 

Reconstructive phase transitions occur when major changes are made in the topology, i.e. when the bond graph is reorganized. The transitions usually observed in structures with lattice-induced strain are displacive and often second order (no latent heat). Reconstructive transitions arise when two quite different structures with the same composition have similar free energies. Unlike the displacive transitions they involve the dissolution of one structure and the recrystallization of a quite different structure. These phase transitions possess a latent heat and often display hysteresis. 

Contrarily to the flatness and horizon problem which have a very similar origin, the unwanted relic problem comes from a very different cause. During the expansion, the Universe becomes colder because of the redshift that radiation experiences. It can happen that during this cooling phase, some phase transition occur, during which some stable objects called topological defects are created. 

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