Uniform Spectral Estimates for Families of Schrödinger Operators with Magnetic Field of Constant Intensity and Applications

DOI10.4067/S0719-06462010000100007zbMATH Open1218.35157arXiv0806.1383OpenAlexW1967305831MaRDI QIDQ3001561

Nicolas Raymond

Publication date: 31 May 2011

Published in: Cubo (Temuco) (Search for Journal in Brave)

Abstract: The aim of this paper is to establish uniform estimates of the spectrum's bottom of the Neumann realization of $(iabla+qA{)}^2$ on a bounded open set $Om$ with smooth boundary when $|ablaimesA|=1$ and $qo+infty$. This problem was motivated by a question occuring in the theory of liquid crystals and appears also in superconductivity questions in large domains.

Full work available at URL: https://arxiv.org/abs/0806.1383

zbMATH Keywords

Schrödinger operatorsmagnetic fieldspectral theorysemiclassical analysisliquid crystalsNeumann Laplacian

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

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