Pinning effects and their breakdown for a Ginzburg–Landau model with normal inclusions
S Alama, L Bronsard - Journal of mathematical physics, 2005 - pubs.aip.org
We study a Ginzburg–Landau model for an inhomogeneous superconductor in the singular
limit as the Ginzburg–Landau parameter κ= 1∕ ϵ→∞. The inhomogeneity is represented
by a potential term V (ψ)= 1 4 (a (x)−∣ ψ∣ 2) 2, with a given smooth function a (x) which is
assumed to become negative in finitely many smooth subdomains, the “normally included”
regions. For bounded applied fields (independent of the Ginzburg–Landau parameter κ=
1∕ ϵ→∞) we show that the normal regions act as “giant vortices,” acquiring large vorticity …
limit as the Ginzburg–Landau parameter κ= 1∕ ϵ→∞. The inhomogeneity is represented
by a potential term V (ψ)= 1 4 (a (x)−∣ ψ∣ 2) 2, with a given smooth function a (x) which is
assumed to become negative in finitely many smooth subdomains, the “normally included”
regions. For bounded applied fields (independent of the Ginzburg–Landau parameter κ=
1∕ ϵ→∞) we show that the normal regions act as “giant vortices,” acquiring large vorticity …
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