Eigenstates of the Neumann Magnetic Laplacian with Vanishing Magnetic Field

TY - JOUR

T1 - Eigenstates of the Neumann Magnetic Laplacian with Vanishing Magnetic Field

AU - Miqueu, Jean Philippe

PY - 2018/7/1

Y1 - 2018/7/1

N2 - This paper is devoted to the spectral analysis of the magnetic Laplacian with semiclassical parameter h> 0 , defined on a bounded and regular domain Ω of R2 with Neumann magnetic boundary condition, in the case when the magnetic field vanishes along a smooth curve intersecting ∂Ω. We investigate the behavior of the eigenvalues and the associated eigenfunctions when the semiclassical parameter h tends to 0. We provide a one term asymptotic of the first eigenvalue as well as a full asymptotic expansion of the bottom of the spectrum as h→ 0.

AB - This paper is devoted to the spectral analysis of the magnetic Laplacian with semiclassical parameter h> 0 , defined on a bounded and regular domain Ω of R2 with Neumann magnetic boundary condition, in the case when the magnetic field vanishes along a smooth curve intersecting ∂Ω. We investigate the behavior of the eigenvalues and the associated eigenfunctions when the semiclassical parameter h tends to 0. We provide a one term asymptotic of the first eigenvalue as well as a full asymptotic expansion of the bottom of the spectrum as h→ 0.

UR - http://www.scopus.com/inward/record.url?scp=85045760512&partnerID=8YFLogxK

U2 - 10.1007/s00023-018-0681-7

DO - 10.1007/s00023-018-0681-7

M3 - Journal article

AN - SCOPUS:85045760512

SN - 1424-0637

VL - 19

SP - 2021

EP - 2068

JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 7

ER -