Localized eigenfunctions in Šeba billiards

J. P. Keating; J. Marklof; B. Winn

doi:10.1063/1.3393884

Localized eigenfunctions in Šeba billiards

J. P. Keating, J. Marklof, B. Winn^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

8 Citations (Scopus)

Abstract

We describe some new families of quasimodes for the Laplacian perturbed by the addition of a potential formally described by a Dirac delta function. As an application, we find, under some additional hypotheses on the spectrum, subsequences of eigenfunctions of Šeba billiards that localize around a pair of unperturbed eigenfunctions.

Original language	English
Article number	050004JMP
Journal	Journal of Mathematical Physics
Volume	51
Issue number	6
DOIs	https://doi.org/10.1063/1.3393884
Publication status	Published - 1 Jun 2010

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title = "Localized eigenfunctions in {\v S}eba billiards",

abstract = "We describe some new families of quasimodes for the Laplacian perturbed by the addition of a potential formally described by a Dirac delta function. As an application, we find, under some additional hypotheses on the spectrum, subsequences of eigenfunctions of {\v S}eba billiards that localize around a pair of unperturbed eigenfunctions.",

author = "Keating, {J. P.} and J. Marklof and B. Winn",

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T1 - Localized eigenfunctions in Šeba billiards

AU - Keating, J. P.

AU - Marklof, J.

AU - Winn, B.

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N2 - We describe some new families of quasimodes for the Laplacian perturbed by the addition of a potential formally described by a Dirac delta function. As an application, we find, under some additional hypotheses on the spectrum, subsequences of eigenfunctions of Šeba billiards that localize around a pair of unperturbed eigenfunctions.

AB - We describe some new families of quasimodes for the Laplacian perturbed by the addition of a potential formally described by a Dirac delta function. As an application, we find, under some additional hypotheses on the spectrum, subsequences of eigenfunctions of Šeba billiards that localize around a pair of unperturbed eigenfunctions.

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U2 - 10.1063/1.3393884

DO - 10.1063/1.3393884

M3 - Article (Academic Journal)

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VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

M1 - 050004JMP

ER -

Localized eigenfunctions in Šeba billiards

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