Laboratoire de Mathématiques Jean Leray

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20022009

most citedThe d-bar approach to approximate inverse scattering at fixed energy in three dimensions

76 citations

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24 papers

math.AG2005

Geometry over composition algebras : projective geometry

Pierre-Emmanuel Chaput

The purpose of this article is to introduce projective geometry over composition algebras : the equivalent of projective spaces and Grassmannians over them are defined. It will fol…

math-ph2005★ 18 cited

Quadratic Quantum Hamiltonians revisited

Monique Combescure, Didier Robert

Time dependent quadratic Hamiltonians are well known as well in classical mechanics and in quantum mechanics. In particular for them the correspondance between classical and quantu…

math-ph2005

Reduced Gutzwiller formula with symmetry: case of a Lie group

Roch Cassanas

We consider a classical Hamiltonian $H$ on $R^{2 d}$ , invariant by a Lie group of symmetry $G$ , whose Weyl quantization $H^$ is a selfadjoint operator on $L^2(\mathbb{…

math-ph2005

The dressed mobile atoms and ions

Laurent Amour, Benoit Grebert, Jean-Claude Guillot

We consider free atoms and ions in $R^{3}$ interacting with the quantized electromagnetic field. Because of the translation invariance we consider the reduced hamiltonian associated…

math-ph2005

Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems

Jean Dolbeault, Patricio Felmer, Michael Loss +1

We prove a Lieb-Thirring type inequality for potentials such that the associated Schrödinger operator has a pure discrete spectrum made of an unbounded sequence of eigenvalues. Thi…

math-ph2005

An inverse scattering problem for short-range systems in a time-periodic electric field

François Nicoleau

We consider the time-dependent Hamiltonian $H (t) = \frac{1}{2} p^{2} - E (t) \cdot x + V (t, x)$ on $L^{2} (R^{n})$ , where the external electric field $E (t)$ and the short-range electric poten…