# Ginzburg-Landau theory

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## Ginzburg-Landau theory

[′ginz·bərg ′lan·dau̇ ‚thē·ə·rē]
(cryogenics)
A phenomenological theory of superconductivity which accounts for the coherence length; the ordered state of a superconductor is described by a complex order parameter which is similar to a Schrödinger wave function, but describes all the condensed superelectrons, rather than a single charged particle. Also known as Landau-Ginzburg theory.
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As a result, the overall time consumption of Newton's method for the Ginzburg-Landau equation is reduced by roughly 40%.
2 deal with the numerical treatment of nonlinear Schrodinger equations in general and the Ginzburg-Landau equation in particular.
1) is the Ginzburg-Landau equation that models supercurrent density for extreme-type-II superconductors.
This method has been applied to the specialization of the Ginzburg-Landau equations (3.
The authors could show that for the particular case of the Ginzburg-Landau equations, the deflation strategy reduces the effective run time of a linear solve by up to 40% (cf.
Weakly nonlocal irreversible thermodynamics--the Ginzburg-Landau equation.
It is known that Ginzburg-Landau equation exhibits fractal character, which implies that quantization could happen at any scale, supporting topological interpretation of quantized vortices [4].
3 Schrodinger equation derived from Ginzburg-Landau equation
It is known that Ginzburg-Landau equation can be used to explain various aspects of superfluid dynamics [16, 17].
In other words, we conclude that it is possible to rederive Schrodinger equation from simplification of (Gross- Pitaevskii) Ginzburg-Landau equation for superfluid dynamics [40], in the limit of small screening parameter, [delta].
one can derive the Ginzburg-Landau equations [30-31]
Among the topics are the resolution of smooth group actions, artificial holes, Sobolev mapping properties of the scattering transform for the Schrodinger equation, normalized differentials on families of curves of infinite genus, characteristic classes and zeroth-order pseudodifferential operators, and Abrikosov lattive solutions of the Ginzburg-Landau equations.

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