Hearing the zero locus of a magnetic field
type: Item
instance of: scholarly article
title: Hearing the zero locus of a magnetic field
zbMATH Open document ID: 0827.58076
DOI: 10.1007/BF02101848
author: Richard Montgomery
published in: Communications in Mathematical Physics
publication date: 1995-12-04T00:00:00Z
review text: This is a study of a two-dimensional particle in a magmetic field that vanishes nondegenerately on a closed curve. The author shows that the ground state concentrates on this curve in the limit \(e/\hbar \to \infty\) where \(e\) is the charge and that the ground state energy grows as \((e/\hbar)^{2/3}\). If the gradient of the magnetic field is of constant magnitude \(b_0\) along its zero locus, then every energy level has asymptotes \((e/\hbar)^{2/3} (b_0)^{2/3}E_* + O(1)\) where \(E_* \approx 0.5698\) is the infimum of the ground state energies of the anharmonic oscillator family \(- {d^2\over dy^2} + ({1\over 2} y^2 - \beta)^2\) where \(\beta\) is a parameter.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 82D40
zbMATH DE Number: 778978
zbMATH Keywords: quantum particle
zbMATH Keywords: magmetic field
zbMATH Keywords: ground state
reviewed by: Chandra Shekhar Sharma
MaRDI profile type: Publication
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Wikidata QID: Q126116705
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description: scientific article; zbMATH DE number 778978