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- W4386395884 abstract "Let $Omega subset mathbb{R}^d$ and consider the magnetic Laplace operator given by $ H(A) = left(- inabla - A(x)right)^2$, where $A:Omega rightarrow mathbb{R}^d$, subject to Dirichlet eigenfunction. This operator can, for certain vector fields $A$, have eigenfunctions $H(A) psi = lambda psi$ that are highly localized in a small region of $Omega$. The main goal of this paper is to show that if $|psi|$ assumes its maximum in $x_0 in Omega$, then $A$ behaves `almost' like a conservative vector field in a $1/sqrt{lambda}-$neighborhood of $x_0$ in a precise sense: we expect localization in regions where $left|mbox{curl} A right|$ is small. The result is illustrated with numerical examples." @default.
- W4386395884 created "2023-09-03" @default.
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- W4386395884 date "2023-08-30" @default.
- W4386395884 modified "2023-09-27" @default.
- W4386395884 title "On localization of eigenfunctions of the magnetic Laplacian" @default.
- W4386395884 doi "https://doi.org/10.48550/arxiv.2308.15994" @default.
- W4386395884 hasPublicationYear "2023" @default.
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