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Displaying similar documents to “Confining quantum particles with a purely magnetic field”

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...

Strong diamagnetism for general domains and application

Soeren Fournais, Bernard Helffer (2007)

Annales de l’institut Fourier

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We consider the Neumann Laplacian with constant magnetic field on a regular domain in ℝ 2 . Let B be the strength of the magnetic field and let λ 1 ( B ) be the first eigenvalue of this Laplacian. It is proved that B ↦ λ 1 ( B ) is monotone increasing for large B . Together with previous results of the authors, this implies the coincidence of all the “third” critical fields for strongly type 2 superconductors.

Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials

Pascal Auscher, Besma Ben Ali (2007)

Annales de l’institut Fourier

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We show various L p estimates for Schrödinger operators - Δ + V on ℝ n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of - Δ + V and their gradients.

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...