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Large Field Asymptotics of the Magnetic Schrödinger Operator: The Case of Dimension 2

  • Søren Fournais
  • Bernard Helffer
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 77)

Abstract

In this chapter, we study the asymptotics of the ground state energy of the magnetic Neumann operator \(P^N_{B{\bf A},\Omega}\) as the field strength B tends to infinity. We also obtain the localization properties of the ground state. These results are combined to analyze the question of the monotonicity of the ground state energy.

Keywords

Ground State Energy Boundary Curvature Trial Function Semiclassical Limit Magnetic Ground State 
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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesAarhus UniversityAarhus CDenmark
  2. 2.Département de MathématiquesUniversité Paris-Sud and CNRSOrsay CedexFrance

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