Effective operators on an attractive magnetic edge

Soren Fournais; Bernard Helffer; Ayman Kachmar; Nicolas Raymond

doi:10.5802/jep.236

Effective operators on an attractive magnetic edge

Soren Fournais, Bernard Helffer, Ayman Kachmar, Nicolas Raymond

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

3 Citations (Scopus)

51 Downloads (Pure)

Abstract

The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontinuous along a smooth closed curve, thereby producing an attractive magnetic edge. Various accurate spectral asymptotics are established by means of a dimensional reduction involving a microlocal phase space localization allowing to deal with the discontinuity of the field.

Original language	English
Journal	Journal de l'Ecole Polytechnique - Mathematiques
Volume	10
Pages (from-to)	917-944
Number of pages	28
ISSN	2429-7100
DOIs	https://doi.org/10.5802/jep.236
Publication status	Published - 2023

Bibliographical note

Publisher Copyright:
© 2023 Ecole Polytechnique. All rights reserved.

Keywords

discontinuous magnetic field
Magnetic Laplacian
semiclassical analysis
spectrum

Access to Document

10.5802/jep.236Licence: CC BY

FulltextFinal published version, 1.16 MBLicence: CC BY

Cite this

@article{0351dce4153d404bae181744d1995799,

title = "Effective operators on an attractive magnetic edge",

abstract = "The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontinuous along a smooth closed curve, thereby producing an attractive magnetic edge. Various accurate spectral asymptotics are established by means of a dimensional reduction involving a microlocal phase space localization allowing to deal with the discontinuity of the field.",

keywords = "discontinuous magnetic field, Magnetic Laplacian, semiclassical analysis, spectrum",

author = "Soren Fournais and Bernard Helffer and Ayman Kachmar and Nicolas Raymond",

year = "2023",

doi = "10.5802/jep.236",

language = "English",

volume = "10",

pages = "917--944",

journal = "Journal de l'Ecole Polytechnique - Mathematiques",

issn = "2429-7100",

publisher = "Ecole Polytechnique",

}

TY - JOUR

T1 - Effective operators on an attractive magnetic edge

AU - Fournais, Soren

AU - Helffer, Bernard

AU - Kachmar, Ayman

AU - Raymond, Nicolas

PY - 2023

Y1 - 2023

N2 - The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontinuous along a smooth closed curve, thereby producing an attractive magnetic edge. Various accurate spectral asymptotics are established by means of a dimensional reduction involving a microlocal phase space localization allowing to deal with the discontinuity of the field.

AB - The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontinuous along a smooth closed curve, thereby producing an attractive magnetic edge. Various accurate spectral asymptotics are established by means of a dimensional reduction involving a microlocal phase space localization allowing to deal with the discontinuity of the field.

KW - discontinuous magnetic field

KW - Magnetic Laplacian

KW - semiclassical analysis

KW - spectrum

UR - http://www.scopus.com/inward/record.url?scp=85161024089&partnerID=8YFLogxK

U2 - 10.5802/jep.236

DO - 10.5802/jep.236

M3 - Journal article

AN - SCOPUS:85161024089

VL - 10

SP - 917

EP - 944

JO - Journal de l'Ecole Polytechnique - Mathematiques

JF - Journal de l'Ecole Polytechnique - Mathematiques

SN - 2429-7100

ER -

Effective operators on an attractive magnetic edge

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Cite this