Phase transition nonequilibrium

Quantum Field Theory for Nonequilibrium Phase Transitions... 

Quantum field theory for nonequilibrium phase transitions... 

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. 

To describe nonequilibrium phase transitions, there have been developed many methods such as the closed-time path integral by Schwinger and Keldysh (J. Schwinger et.al., 1961), the Hartree-Fock or mean field method (A. Ringwald, 1987), and the l/lV-expansion method (F. Cooper et.al., 1997 2000). In this talk, we shall employ the so-called Liouville-von Neumann (LvN) method to describe nonequilibrium phase transitions (S.P. Kim et.al., 2000 2002 2001 S.P. Kim et.al., 2003). The LvN method is a canonical method that first finds invariant operators for the quantum LvN equation and then solves exactly the... 

As a field model for nonequilibrium phase transitions of second order, we consider a scalar field potential... 

We now turn to the potential (4) for nonequilibrium phase transition. We separate the Hamiltonian density H into a quadratic part Ho and a perturbation part Hp ... 

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... 

Haken, J. (1978). Synergetics. An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology. Berlin Springer-Verlag. 

TNC.53. 1. Prigogine and J. W. Turner, Nonequilibrium phase transitions, Proc. Karcher Symp. Structural Aspects of Homogeneous, Heterogeneous and Biological Catalysis, University Oklahoma, American Crystallographic Association, pp. 103—141. 

TNC.54. 1. Prigogine, New aspects of chemical kinetics and nonequilibrium phase transitions. Proceedings of Symposium Structure and Dynamics in Chemistry, Uppsala, 1977, P. Ahlberg and L.-O. Sundelof, eds., pp. 172-186. 

TNC.64. M. Malek-Mansour, G. Nicolis, and I. Prigogine, Nonequilibrium phase transitions in chemical systems, in Thermodynamics and Kinetics of Biological Processes, 1. Lamprecht and A. 1. Zotin, eds., W. de Gmyter, Berlin, 1982, pp. 75-103. 

Damaskin and Baturina [171] have studied unstable states during coumarin adsorption on mercury electrode. These instabilities were attributed to the nonequilibrium phase transitions in the adsorption layer, during which the orientation of coumarin molecules changed at the electrode surface. 

Three Zero-One Laws and Nonequilibrium Phase Transitions in Multiscale Systems... 

In multiscale asymptotic analysis of reaction network we found several very attractive zero-one laws. First of all, components eigenvectors are close to 0 or +1. This law together with two other zero-one laws are discussed in Section 6 "Three zero-one laws and nonequilibrium phase transitions in multiscale systems". 

THREE ZERO-ONE LAWS AND NONEQUILIBRIUM PHASE TRANSITIONS IN MULTISCALE SYSTEMS... 

The conference was divided into four parts to each of which a full day was devoted the first one treated Equilibrium Statistical Mechanics, with special regard to The Theory of Critical Phenomena the second part regarded Nonequilibrium Statistical Mechanics. Cooperative Phenomena the third one, The Macroscopic Approach to Coherent Behavior in Far Equilibrium Conditions and the fourth and last, Fluctuation Theory and Nonequilibrium Phase Transitions. ... 

Dynamical Self-Organization. When the parameter X passes slowly through X (l),the bifurcation picture of the previous section accurateiy describes the system. However, in Fucus, and probably in many other examples, this time scale separation between the characteristic time on which X varies and the time to obtain the patterned state does not hold. Thus a dynamical theory allowing for the interplay of these two time scales is required to characterize the developmental scenario. A natural formalism to describe this process is that of time dependent Ginzburg-Landau (tdgl) equations used successfully in other contexts of nonequilibrium phase transitions (27). 

Matheson, I., Walls, D., and Gardiner, C., Stochastic models of first-order nonequilibrium phase transitions in chemical reactions, Journal of Statistical Physics, Vol. 12, 1975, pp. 21-34. 

E. Scholl Nonequilibrium Phase Transitions in SemiconductorsspaX (Springer, Berlin, 1987). 

Such structures by the way are consistent with the ideas proposed by Frohlich in the sense that they can be switched to a coherent mode. A nonequilibrium phase transition that manifest itself as a limit cycle is a familiar example of such a phenomenon.The possible role of these types of nonequilibrium phase transitions in governing the interaction of external electromagnetic fields with biological systems has been discussed by Kaiser. 

Nonequilibrium Phase Transitions and Self-Oi ganization in Physics, Chemistry and Biology... 

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