Magnetic spectral bounds on starlike plane domains

R. S. Laugesen, B. A. Siudeja

Research output: Contribution to journalArticle

Abstract

We develop sharp upper bounds for energy levels of the magnetic Laplacian on starlike plane domains, under either Dirichlet or Neumann boundary conditions and assuming a constant magnetic field in the transverse direction. Our main result says that σn j=1 ψ(λjA/G) is maximal for a disk whenever ψ is concave increasing, n . 1, the domain has area A, and λj is the jth Dirichlet eigenvalue of the magnetic Laplacian iδ + B/2A(-x2, x1)2. Here the flux β is constant, and the scale invariant factor G penalizes deviations from roundness, meaning G > 1 for all domains and G = 1 for disks.

Original languageEnglish (US)
Pages (from-to)670-689
Number of pages20
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume21
Issue number3
DOIs
StatePublished - Jul 1 2015

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Keywords

  • Heat trace
  • Isoperimetric
  • Partition function
  • Pauli operator
  • Spectral zeta

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

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