THIN DOMAIN LIMIT AND COUNTEREXAMPLES TO STRONG DIAMAGNETISM

Bernard Helffer (1) , Ayman Kachmar (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]

We study the magnetic Laplacian and the Ginzburg-Landau functional in a thin planar, smooth, tubular domain and with a uniform applied magnetic field. We provide counterexamples to strong diamagnetism, and as a consequence, we prove that the transition from the superconducting to the normal state is non-monotone. In some non-linear regime, we determine the structure of the order parameter and compute the super-current along the boundary of the sample. Our results are in agreement with what was observed in the Little-Parks experiment, for a thin cylindrical sample.

Domaines: Mathématiques [math]; Physique mathématique [math-ph]

Bernard Helffer, Ayman Kachmar. THIN DOMAIN LIMIT AND COUNTEREXAMPLES TO STRONG DIAMAGNETISM. 2019. ⟨hal-02369653⟩