Displaying similar documents to “Schrödinger operator with magnetic field in domain with corners”

Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential

Frédéric Hérau (2002)

Journées équations aux dérivées partielles

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We consider the Fokker-Planck equation with a confining or anti-confining potential which behaves at infinity like a possibly high degree homogeneous function. Hypoellipticity techniques provide the well-posedness of the weak-Cauchy problem in both cases as well as instantaneous smoothing and exponential trend to equilibrium. Lower and upper bounds for the rate of convergence to equilibrium are obtained in terms of the lowest positive eigenvalue of the corresponding Witten laplacian,...

Scattering amplitude for the Schrödinger equation with strong magnetic field

Laurent Michel (2005)

Journées Équations aux dérivées partielles

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In this note, we study the scattering amplitude for the Schrödinger equation with constant magnetic field. We consider the case where the strengh of the magnetic field goes to infinity and we discuss the competition between the magnetic and the electrostatic effects.

On spectral problems related to a time dependent model in superconductivity with electric current

Bernard Helffer (2009)

Journées Équations aux dérivées partielles

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This lecture is mainly inspired by a paper of Y. Almog appearing last year at Siam J. Math. Anal. Our goal here is first to discuss in detail the simplest models which we think are enlightning for understanding the role of the pseudospectra in this question and secondly to present proofs which will have some general character and will for example apply in a more physical model, for which we have obtained recently results together with Y. Almog and X. Pan.