One-dimensional Ginzburg-Landau model in a random external field: Equivalent quantum mechanics

1992 ◽  
Vol 45 (2) ◽  
pp. 814-818 ◽  
Author(s):  
Y. S. Parmar ◽  
J. K. Bhattacharjee
Keyword(s):  
Quantum Mechanics ◽  
External Field ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Equivalent Quantum ◽  
Random External Field

On the minimizers of the Ginzburg–Landau energy for high kappa: the one-dimensional case

1997 ◽  
Vol 8 (4) ◽  
pp. 331-345 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behaviour ◽  
Dimensional Case ◽  
Numerical Computations ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Landau Parameter ◽  
Convergence Results ◽  
The One

The Ginzburg–Landau model for superconductivity is examined in the one-dimensional case. First, putting the Ginzburg–Landau parameter κ formally equal to infinity, the existence of a minimizer of this reduced Ginzburg–Landau energy is proved. Then asymptotic behaviour for large κ of minimizers of the full Ginzburg–Landau energy is analysed and different convergence results are obtained, according to the exterior magnetic field. Numerical computations illustrate the various behaviours.

Global bifurcation structure of a one-dimensional Ginzburg–Landau model

2005 ◽  
Vol 46 (9) ◽  
pp. 095111 ◽  
Author(s):  
Satoshi Kosugi ◽  
Yoshihisa Morita ◽  
Shoji Yotsutani
Keyword(s):  
Global Bifurcation ◽  
Bifurcation Structure ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional

scholarly journals LORENTZ SPACE ESTIMATES FOR THE COULOMBIAN RENORMALIZED ENERGY

2012 ◽  
Vol 14 (04) ◽  
pp. 1250027 ◽  
Author(s):  
SYLVIA SERFATY ◽  
IAN TICE
Keyword(s):  
Lorentz Space ◽  
Vortex Lattice ◽  
Construction Method ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Optimal Estimates ◽  
Renormalized Energy ◽  
Funct Anal ◽  
Math Phys

In this paper we obtain optimal estimates for the "currents" associated to point masses in the plane, in terms of the Coulombian renormalized energy of Sandier–Serfaty [From the Ginzburg–Landau model to vortex lattice problems, to appear in Comm. Math. Phys. (2012); One-dimensional log gases and the renormalized energy, in preparation]. To derive the estimates, we use a technique that we introduced in [Lorentz space estimates for the Ginzburg–Landau energy, J. Funct. Anal. 254(3) (2008) 773–825], which couples the "ball construction method" to estimates in the Lorentz space L2,∞.

scholarly journals PHASE DIAGRAMS OF ONE-DIMENSIONAL MODELS UNDER STRONG RANDOM EXTERNAL FIELD

2003 ◽  
Vol 17 (30) ◽  
pp. 5781-5794 ◽  
Author(s):  
AZER KERIMOV
Keyword(s):  
External Field ◽  
Phase Diagrams ◽  
Statistical Physics ◽  
Gibbs State ◽  
One Dimensional ◽  
Dimensional Models ◽  
Random External Field

We consider one-dimensional models of classical statistical physics and prove that at each fixed value of the temperature for all realizations of additional sufficiently strong random external field the limiting Gibbs state is unique.

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