Computations of the first eigenpairs for the Schrödinger operator with magnetic field, Comput. Methods Appl. Mech. Engrg, vol.196, pp.3841-3858, 2007. ,
Curvature induced magnetic bound states: towards the magnetic tunneling effect, J. E. D. P, 2016. ,
, Magnetic WKB constructions. Arch. Ration. Mech. Anal, vol.221, issue.2, pp.817-891, 2016.
Semiclassical tunneling and magnetic flux effects on the circle, J. Spectr. Theory, vol.7, issue.3, pp.771-796, 2017. ,
Eigenvalues variation. I. Neumann problem for Sturm-Liouville operators, J. Differential Equations, vol.104, issue.2, pp.243-262, 1993. ,
Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian, Ann. Inst. Fourier (Grenoble), vol.56, issue.1, pp.1-67, 2006. ,
Spectral methods in surface superconductivity, Nonlinear Differential Equations and their Applications, vol.77, 2010. ,
A mathematical approach to the effective Hamiltonian in perturbed periodic problems, Comm. Math. Phys, vol.142, issue.2, pp.217-244, 1991. ,
Double wells, Comm. Math. Phys, vol.75, issue.3, pp.239-261, 1980. ,
Tunneling for the Robin Laplacian in smooth planar domains, Commun. Contemp. Math, vol.19, issue.1, p.38, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01198585
Magnetic bottles in connection with superconductivity, J. Funct. Anal, vol.185, issue.2, pp.604-680, 2001. ,
Multiple wells in the semiclassical limit, I. Comm. Partial Differential Equations, vol.9, issue.4, pp.337-408, 1984. ,
Multiple wells in the semiclassical limit. III. Interaction through nonresonant wells, Math. Nachr, vol.124, pp.263-313, 1985. ,
Puits multiples en limite semi-classique. II. Interaction moléculaire, Symétries. Perturbation. Ann. Inst. H. Poincaré Phys. Théor, vol.42, issue.2, pp.127-212, 1985. ,
Puits multiples en mécanique semi-classique. IV. Étude du complexe de Witten, Comm. Partial Differential Equations, vol.10, issue.3, pp.245-340, 1985. ,
Puits multiples en mécanique semi-classique. V. Étude des minipuits, Current topics in partial differential equations, pp.133-186, 1986. ,
Effet tunnel pour l'équation de Schrödinger avec champ magnétique, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.14, issue.4, pp.625-657, 1987. ,
Puits multiples en mécanique semi-classique. VI. Cas des puits sous-variétés, Ann. Inst. H. Poincaré Phys. Théor, vol.46, issue.4, pp.353-372, 1987. ,
Tunnel effect in a shrinking shell enlacing a magnetic field, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01582532
Formules de Weyl par réduction de dimension. Applications à des Laplaciens électro-magnétiques, 2018. ,
Développements asymptotiques et effet tunnel dans l'approximation de Born-Oppenheimer, Ann. Inst. H. Poincaré Phys. Théor, vol.50, issue.3, pp.239-257, 1989. ,
A general effective Hamiltonian method, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl, vol.18, issue.3, pp.269-277, 2007. ,
Comportement semi-classique pour l'opérateur de Schrödinger à potentiel périodique, J. Funct. Anal, vol.72, issue.1, pp.65-93, 1987. ,
Bound states of the magnetic Schrödinger operator, EMS Tracts in Mathematics, vol.27, 2017. ,
Analyse semi-classique de l'effet tunnel, Séminaire Bourbaki, issue.5, p.86, 1985. ,
Semiclassical analysis of low lying eigenvalues. I. Nondegenerate minima: asymptotic expansions, Ann. Inst. H. Poincaré Sect. A (N.S.), vol.38, issue.3, pp.295-308, 1983. ,
Semiclassical analysis of low lying eigenvalues, II. Tunneling. Ann. of Math, vol.120, issue.2, pp.89-118, 1984. ,
Semiclassical analysis of low lying eigenvalues. III. Width of the ground state band in strongly coupled solids, Ann. Physics, vol.158, issue.2, pp.415-420, 1984. ,
Semiclassical analysis of low lying eigenvalues. IV. The flea on the elephant, J. Funct. Anal, vol.63, issue.1, pp.123-136, 1985. ,
CNRS, 2 rue de la Houssinière, BP 92208, F-44322 Nantes cedex 3, France E-mail address: herau@univ-nantes.fr (N. Raymond) Laboratoire Angevin de Recherche en Mathématiques, LAREMA, UMR 6093, UNIV Angers, Département de mathématiques et applications, École normale supérieure, CNRS, Université PSL, F-75005 ,