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Impossible Einstein-Weyl geometries

Eastwood, Michael (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

In the joint paper of the author with K. P. Tod [J. Reine Angew. Math. 491, 183-198 (1997; Zbl 0876.53029)] they showed all local solutions of the Einstein-Weyl equations in three dimensions, where the background metric is homogeneous with unimodular isometry group. In particular, they proved that there are no solutions with Nil or Sol as background metric. In this note, these two special cases are presented.

Index and dynamics of quantized contact transformations

Steven Zelditch (1997)

Annales de l'institut Fourier

Quantized contact transformations are Toeplitz operators over a contact manifold ( X , α ) of the form U χ = Π A χ Π , where Π : H 2 ( X ) L 2 ( X ) is a Szegö projector, where χ is a contact transformation and where A is a pseudodifferential operator over X . They provide a flexible alternative to the Kähler quantization of symplectic maps, and encompass many of the examples in the physics literature, e.g. quantized cat maps and kicked rotors. The index problem is to determine ind ( U χ ) when the principal symbol is unitary, or equivalently to determine...

Inégalités de résolvante pour l’opérateur de Schrödinger avec potentiel multipolaire critique

Thomas Duyckaerts (2006)

Bulletin de la Société Mathématique de France

On étudie un opérateur de la forme - Δ + V sur d , où V est un potentiel admettant plusieurs pôles en a / r 2 . Plus précisément, on démontre l’estimation de résolvante tronquée à hautes fréquences, classique dans les cas non-captifs, et qui implique l’effet régularisant standard pour l’équation de Schrödinger correspondante. La preuve est basée sur l’introduction d’une mesure de défaut micro-locale semi-classique. On démontre également, dans le même contexte, des inégalités de Strichartz pour l’équation de Schrödinger....

Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits

Alice Barbara Tumpach (2009)

Annales de l’institut Fourier

In this paper, we construct a hyperkähler structure on the complexification 𝒪 of any Hermitian symmetric affine coadjoint orbit 𝒪 of a semi-simple L * -group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of 𝒪 . By a relevant identification of the complex orbit 𝒪 with the cotangent space T 𝒪 of 𝒪 induced by Mostow’s decomposition theorem, this leads to the existence of a hyperkähler structure on T 𝒪 compatible with...

Instabilité spectrale semiclassique pour des opérateurs non-autoadjoints I : un modèle

Mildred Hager (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Dans ce travail, nous considérons un opérateur différentiel simple ainsi que des perturbations. Alors que le spectre de l’opérateur non-perturbé est confiné à une droite à l’intérieur du pseudospectre, nous montrons pour les opérateurs perturbés que les valeurs propres se distribuent à l’intérieur du pseudospectre d’après une loi de Weyl.

Instanton-anti-instanton solutions of discrete Yang-Mills equations

Volodymyr Sushch (2012)

Mathematica Bohemica

We study a discrete model of the S U ( 2 ) Yang-Mills equations on a combinatorial analog of 4 . Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both the techniques of a double complex and the quaternionic approach.

Instruments and mutual entropies in quantum information

Alberto Barchielli, Giancarlo Lupieri (2006)

Banach Center Publications

General quantum measurements are represented by instruments. In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a posteriori state as output. Then, by using mutual entropies on von Neumann algebras and the identification of instruments and channels, many old and new informational inequalities are obtained in a unified manner. Such inequalities involve various quantities which characterize...

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