Diamagnetism versus Robin condition and concentration of ground states

2015/07/29 by Ali Kachmar, A. Kachmar, Kachmar, A.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP

paper · pdf · doi:10.48550/arxiv.1507.08016

arxiv created 2015/07/29 · openalex publication_date 2015/07/29 · arxiv updated 2015/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We estimate the ground state energy for the magnetic Laplacian with a Robin condition. In a special asymptotic limit, we find that the magnetic field does not contribute to the two-term expansion of the ground state energy, thereby proving that the Robin condition weakens diamagnetism. We discuss a semi-classical version of the operator and prove that the ground states concentrate near the boundary points of maximal curvature.

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