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<p>We derive a three-term asymptotic expansion for the lowest eigenvalue of the magnetic Laplace and Steklov operators in the exterior of the unit disk in the strong magnetic field limit. This improves recent results of Helffer–Nicoleau (2025) based on special function asymptotics, and extends earlier works by Fournais–Helffer (2006), Kachmar (2006), and R. Fahs, L. Treust, N. Raymond, S. Vũ Ngọc (2024). Notably, our analysis reveals how the third term encodes the dependence on the magnetic flux. Finally, we investigate the weak magnetic field limit and establish the flux dependence in the asymptotics of Kachmar–Lotoreichik–Sundqvist (2025).</p>

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Flux Effects on Magnetic Laplace and Steklov Eigenvalues in the Exterior of a Disk

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Bernard Helffer,
  • Ayman Kachmar,
  • François Nicoleau

摘要

We derive a three-term asymptotic expansion for the lowest eigenvalue of the magnetic Laplace and Steklov operators in the exterior of the unit disk in the strong magnetic field limit. This improves recent results of Helffer–Nicoleau (2025) based on special function asymptotics, and extends earlier works by Fournais–Helffer (2006), Kachmar (2006), and R. Fahs, L. Treust, N. Raymond, S. Vũ Ngọc (2024). Notably, our analysis reveals how the third term encodes the dependence on the magnetic flux. Finally, we investigate the weak magnetic field limit and establish the flux dependence in the asymptotics of Kachmar–Lotoreichik–Sundqvist (2025).