Displaying similar documents to “Strong diamagnetism for general domains and application”

Confining quantum particles with a purely magnetic field

Yves Colin de Verdière, Françoise Truc (2010)

Annales de l’institut Fourier

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We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behaviour of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples in the case where the boundary is smooth as well as for polytopes;...

Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian

Soeren Fournais, Bernard Helffer (2006)

Annales de l’institut Fourier

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Motivated by the theory of superconductivity and more precisely by the problem of the onset of superconductivity in dimension two, many papers devoted to the analysis in a semi-classical regime of the lowest eigenvalue of the Schrödinger operator with magnetic field have appeared recently. Here we would like to mention the works by Bernoff-Sternberg, Lu-Pan, Del Pino-Felmer-Sternberg and Helffer-Morame and also Bauman-Phillips-Tang for the case of a disc. In the present paper we settle...

The spectrum of Schrödinger operators with random δ magnetic fields

Takuya Mine, Yuji Nomura (2009)

Annales de l’institut Fourier

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We shall consider the Schrödinger operators on ℝ 2 with the magnetic field given by a nonnegative constant field plus random δ magnetic fields of the Anderson type or of the Poisson-Anderson type. We shall investigate the spectrum of these operators by the method of the admissible potentials by Kirsch-Martinelli. Moreover, we shall prove the lower Landau levels are infinitely degenerated eigenvalues when the constant field is sufficiently large, by estimating the growth order of the eigenfunctions...

Schrödinger operator with magnetic field in domain with corners

Virginie Bonnaillie Noël (2005)

Journées Équations aux dérivées partielles

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We present here a simplified version of results obtained with F. Alouges, M. Dauge, B. Helffer and G. Vial (cf [, , ]). We analyze the Schrödinger operator with magnetic field in an infinite sector. This study allows to determine accurate approximation of the low-lying eigenpairs of the Schrödinger operator in domains with corners. We complete this analysis with numerical experiments.

Fokker-Planck equation in bounded domain

Laurent Chupin (2010)

Annales de l’institut Fourier

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We study the existence and the uniqueness of a solution  ϕ to the linear Fokker-Planck equation - Δ ϕ + div ( ϕ F ) = f in a bounded domain of  ℝ d when F is a “confinement” vector field. This field acting for instance like the inverse of the distance to the boundary. An illustration of the obtained results is given within the framework of fluid mechanics and polymer flows.