A new formula for the energy of bulk superconductivity

TL;DR

This paper introduces a novel formula for the reference energy of bulk superconductivity near the second critical magnetic field, simplifying the calculation by using a linear energy limit over normalized configurations.

Contribution

It provides a new, simplified formula for the reference energy in type II superconductors close to the second critical field, derived as a limit of a linear energy.

Findings

New formula for the reference energy in superconductivity

Energy expressed as a limit of linear configurations

Simplifies previous nonlinear energy calculations

Abstract

The energy of a type II superconductor submitted to an external magnetic field of intensity close to the second critical field is given by the celebrated Abrikosov energy. If the external magnetic field is comparable to and below the second critical field, the energy is given by a reference function obtained as a special (thermodynamic) limit of a non-linear energy. In this note, we give a new formula for this reference energy. In particular, we obtain it as a special limit of a {\it linear} energy defined over configurations normalized in the $L^4$-norm.