Ginzburg-Landau theory

Gompper G and Zsohooke S 1991 Elastio properties of interfaoes in a Ginzburg-Landau theory of swollen mioelles, droplet orystals and lamellar phases Euro. Phys. Lett. 16 731... 

The first step in studying phenomenological theories (Ginzburg-Landau theories and membrane theories) has usually been to minimize the free energy functional of the model. Fluctuations are then included at a later stage, e.g., using Monte Carlo simulations. The latter will be discussed in Sec. V and Chapter 14. 

Ginzburg-Landau theories of amphiphiles have been reviewed at various places [1,25], among others, in Chapter 14 of this book. Hence we shall be brief in this subsection. 

The basic idea of a Ginzburg-Landau theory is to describe the system by a set of spatially varying order parameter fields, typically combinations of densities. One famous example is the one-order-parameter model of Gompper and Schick [173], which uses as the only variable 0, the density difference between oil and water, distributed according to the free energy functional... 

Random interface models for ternary systems share the feature with the Widom model and the one-order-parameter Ginzburg-Landau theory (19) that the density of amphiphiles is not allowed to fluctuate independently, but is entirely determined by the distribution of oil and water. However, in contrast to the Ginzburg-Landau approach, they concentrate on the amphiphilic sheets. Self-assembly of amphiphiles into monolayers of given optimal density is premised, and the free energy of the system is reduced to effective free energies of its internal interfaces. In the same spirit, random interface models for binary systems postulate self-assembly into bilayers and intro-... 

For a recent review on Ginzburg-Landau theories, see G. Gompper. Ber. Bunsenges Phys Chemie i00 264-271, 1996. 

G. Gompper, S. Zschocke. Elastic properties of interface in a Ginzburg-Landau theory of swollen micells, droplet crystals and lamellar phases. Euro-phys Lett 16 13 -136, 1991. 

G. Gompper, M. Kraus. Ginzburg-Landau theory of ternary amphiphilic systems. II. Monte Carlo simulations. Phys Rev E 47 4301- 312, 1993. 

Figure 5. Temperature development of the electronic density of states in fee FeaNi with the temperature dependent input taken from the Ginzburg-Landau theory (magnetic moments are given per atom).

Ginzburg Landau theory of superconductivity Beyond the post Gaussian approximation... 

The Ginzburg-Landau theory for the CFL phase has been derived in Refs. [10, 16-19], The authors of Ref. [19] have taken into account the rotated electromagnetism and the rotation of the star. They conclude that ordinary quantized magnetic vortices are unstable in the CFL phase, but the rotational vortices are topologically stable. They have not considered boundary problems and concluded that the CFL condensate in an external magnetic held behaves like a type I superconductor. 

In this paper we study the distribution of the magnehc held of a neutron star with superconducting CFL quark matter core in the framework of the Ginzburg-Landau theory. We solve the Ginzburg-Landau equations with proper boundary conditions. 

The Ginzburg-Landau theory is equivalent to a mean field theory considering the thermodynamic entity of the dipoles in the mean field of all the others. It is reasonable if the particular... 

A superconductor exhibits perfect conductivity (See Section 7.2) and the Meissner effect (See Section 7.3) below some critical temperature, Tc. The transition from a normal conductor to a superconductor is a second-order, phase-transition which is also well-described by mean-field theory. Note that the mean-field condensation is not a Bose condensation nor does it require and energy gap. The mean-field theory is combined with London-Ginzburg-Landau theory through the concentration of superconducting carriers as follows ... 

Using the potential V(h)°ch2 in Eq. (110), one recognizes that Eq. (110) is formally identical to a Ginzburg-Landau theory of a second-order transition for T>TC(D), with h(x,y) the order parameter field [186,216]. Therefore, it is straightforward to read off the correlation length , associated with this transition at TC(D), namely... 

However, at higher temperatures Jd is reduced. Near Tc, an estimate can be made with the Ginzburg-Landau theory (14) ... 

An alternative approach to such kinematically extended continua is presented by Capriz et al. [9-11] and Svendsen [39, 40]. They introduce scalar-valued order parameters to describe the influence of the microstructure in analogy to the Ginzburg-Landau theory. 

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