The density of superconductivity in the bulk regime

TL;DR

This paper derives a new asymptotic formula for the $L^2$-norm of the Ginzburg-Landau order parameter in the bulk regime, enhancing understanding of superconductivity behavior near the second critical field.

Contribution

It introduces a novel asymptotic formula for the $L^2$-norm of the order parameter, complementing existing results for the $L^4$-norm in the large Ginzburg-Landau parameter limit.

Findings

New asymptotic formula for the $L^2$-norm in the bulk regime

Complementary to Sandier-Serfaty's $L^4$-norm result

Applicable when magnetic field is below the second critical field

Abstract

In the asymptotic limit of a large Ginzburg-Landau parameter, we give a new asymptotic formula for the $L^2$-norm of the Ginzburg-Landau order parameter. The formula is valid in the bulk regime where the intensity of the applied magnetic field is of the same order as the Ginzburg-Landau parameter and strictly below the second critical field. Our formula complements the celebrated one of Sandier-Serfaty for the $L^4$-norm.