An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns
By Pierre Hohenberg, A. Krekhov. 2014
246 citations recorded by the source corpus.
Abstract This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg–Landau theory as a unified language. In the first part, mean-field theory is presented, for both statics and dynamics, and its validity tested self-consistently. As is well known, the mean-field approximation breaks down below four spatial dimensions, where it can be replaced by a scaling phenomenology. The Ginzburg–Landau formalism can then be used to justify the phenomenological theory using the renormalization group, which elucidates the physical and mathematical mechanism for universality. In the second part of the paper it is shown how near pattern forming linear instabilities of dynamical systems, a formally similar Ginzburg–Landau theory can be derived for nonequilibrium macroscopic phenomena. The real and complex Ginzburg–Landau equations thus obtained yield nontrivial solutions of the original dynamical system, valid near the linear instability. Examples of such solutions are plane waves, defects such as dislocations or spirals, and states of temporal or spatiotemporal (extensive) chaos.
Subfields: Computer Networks and Communications, Condensed Matter Physics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/afc0b35a38dfeae619a310a7e8342bcd3c37b9bf
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In Condensed Matter Physics
Citations in the corpus
- An introduction to spontaneous symmetry breaking (2019, background): “extends to dynamical phenomena as well. critical exponent { dynamical It leads to the emergence of dynamical critical exponents for quantities such as damping and relaxation. This is reviewed in Ref. [110,111]. A.4Quantum phase transitions Our discussion of phase transitions in Chapter 5 covered ord”