On the ground state energy for a magnetic Shcr\"odinger operator and the effect of the De Gennes Boundary condition

TL;DR

This paper estimates the ground state energy of a magnetic Schrödinger operator with De Gennes boundary condition in the semi-classical limit and analyzes how this boundary condition influences the localization of the ground state, with implications for superconductivity.

Contribution

It provides new estimates for the ground state energy considering De Gennes boundary conditions and explores their impact on ground state localization in the context of superconductivity.

Findings

De Gennes boundary condition significantly affects ground state localization.

The paper offers semi-classical estimates for the ground state energy.

Localization behavior varies depending on boundary condition strength.

Abstract

Motivated by the Ginzburg-Landau theory of superconductivity, we estimate in the semi-classical limit the ground state energy of a magnetic Schr\"odinger operator with De Gennes boundary condition and we study the localization of the ground state. We exhibit cases when the De Gennes boundary condition has strong effects on this localization.