MAGNETIC WELLS IN DIMENSION THREE

被引：18

作者：

Helffer, Bernard ^{[1
,2
,3
]}

Kordyukov, Yuri ^{[4
]}

Raymond, Nicolas ^{[5
]}

San Vu Ngoc ^{[5
,6
]}

机构：

[1] Univ Paris 11, Dept Math, Bat 425, F-91405 Orsay, France

[2] CNRS, F-91405 Orsay, France

[3] Univ Nantes, Lab Math Jean Leray, 2 Rue Houssiniere,BP 92208, F-44322 Nantes 3, France

[4] Russian Acad Sci, Inst Math, 112 Chernyshevsky Str, Ufa 450008, Russia

[5] Univ Rennes 1, Inst Rech Math Rennes UMR 6625, Campus Beaulieu, F-35042 Rennes, France

[6] Inst Univ France, 1 Rue Descartes, F-75231 Paris 5, France

来源：

ANALYSIS & PDE | 2016年 / 9卷 / 07期

关键词：

magnetic fields; Birkhoff normal forms; microlocal analysis; SCHRODINGER OPERATOR; SEMICLASSICAL ANALYSIS; SPECTRAL ASYMPTOTICS; FIELD; LAPLACIAN;

D O I：

10.2140/apde.2016.9.1575

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with semiclassical asymptotics of the three-dimensional magnetic Laplacian in the presence of magnetic confinement. Using generic assumptions on the geometry of the confinement, we exhibit three semiclassical scales and their corresponding effective quantum Hamiltonians, by means of three microlocal normal forms a la Birkhoff. As a consequence, when the magnetic field admits a unique and nondegenerate minimum, we are able to reduce the spectral analysis of the low-lying eigenvalues to a one-dimensional, h-pseudodifferential operator whose Weyl's symbol admits an asymptotic expansion in powers of h(1/2).

引用

页码：1575 / 1608

页数：34

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