Displaying similar documents to “On spectral problems related to a time dependent model in superconductivity with electric current”

Spectral properties of non-self-adjoint operators

Johannes Sjöstrand (2009)

Journées Équations aux dérivées partielles

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This text contains a slightly expanded version of my 6 hour mini-course at the PDE-meeting in Évian-les-Bains in June 2009. The first part gives some old and recent results on non-self-adjoint differential operators. The second part is devoted to recent results about Weyl distribution of eigenvalues of elliptic operators with small random perturbations. Part III, in collaboration with B. Helffer, gives explicit estimates in the Gearhardt-Prüss theorem for semi-groups.

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.

Local Exchange Potentials for Electronic Structure Calculations

Eric Cancès, Gabriel Stoltz, Gustavo E. Scuseria, Viktor N. Staroverov, Ernest R. Davidson (2009)

MathematicS In Action

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The Hartree-Fock exchange operator is an integral operator arising in the Hartree-Fock model as well as in some instances of the density functional theory. In a number of applications, it is convenient to approximate this integral operator by a multiplication operator, i.e. by a local potential. This article presents a detailed analysis of the mathematical properties of various local approximations to the nonlocal Hartree-Fock exchange operator including the Slater potential, the optimized...

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,...