Published In
Reports on Mathematical Physics
Document Type
Pre-Print
Publication Date
10-1-2024
Subjects
Eigenfunctions -- Mathematical and Computational Physics, Laplacian matrices
Abstract
Let Ω ⊂ ℝd and consider the magnetic Laplace operator given by H(A) = (–i∇ – A(x))2, where A : Ω → ℝd, subject to Dirichlet boundary conditions. For certain vector fields A, this operator can have eigenfunctions, H(A)ψ = λψ, that are highly localized in a small region of Ω. The main goal of this paper is to show that if |ψ| assumes its maximum at x0 ∈ Ω, then A behaves 'almost' like a conservative vector field in a -neighborhood of x0 in a precise sense. In particular, we expect localization in regions where |curl A| is small. The result is illustrated with numerical examples.
Rights
© Copyright the author(s) 2024
Persistent Identifier
https://archives.pdx.edu/ds/psu/42933
Citation Details
Published as: On localization of eigenfunctions of the magnetic Laplacian. Reports on Mathematical Physics, 94(2), 235-257.
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: On localization of eigenfunctions of the magnetic Laplacian. Reports on Mathematical Physics, 94(2), 235-257.