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<p>Inspired by a paper by Chakradhar, Gittins, Habib and Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator on the disk tends to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2009_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(+\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>+</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation> as the magnetic field tends to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2009_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(+\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>+</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>. This is an important step towards the analysis of the curvature effect in the case of general domains in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2009_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb R^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">R</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>.</p>

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On the Magnetic Dirichlet to Neumann Operator on the Disk: Strong Diamagnetism and Strong Magnetic Field Limit

  • 期刊论文

  • 发表日期：

    2025年4月22日

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  • Bernard Helffer,
  • François Nicoleau

摘要

Inspired by a paper by Chakradhar, Gittins, Habib and Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator on the disk tends to \(+\infty \) + ∞ as the magnetic field tends to \(+\infty \) + ∞ . This is an important step towards the analysis of the curvature effect in the case of general domains in \(\mathbb R^2\) R 2 .