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In this paper, we study the linear Schrödinger equation over the d-dimensional torus, with small values of the perturbing potential. We consider numerical approximations of the associated solutions obtained by a symplectic splitting method (to discretize the time variable) in combination with the Fast Fourier Transform algorithm (to discretize the space variable). In this fully discrete setting, we prove that the regularity of the initial datum is preserved over long times, i.e. times that are...

Propagation of singularities in many-body scattering in the presence of bound states

András Vasy (1999)

Journées équations aux dérivées partielles

In these lecture notes we describe the propagation of singularities of tempered distributional solutions $u \in 𝒮^{'}$ of $(H - λ) u = 0$ , where $H$ is a many-body hamiltonian $H = Δ + V$ , $Δ \geq 0$ , $V = \sum_{a} V_{a}$ , and $λ$ is not a threshold of $H$ , under the assumption that the inter-particle (e.g. two-body) interactions $V_{a}$ are real-valued polyhomogeneous symbols of order $- 1$ (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is then that the...

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Prolongement méromorphe de la matrice de diffusion pour les problèmes à $N$ corps à longue portée

Prolongement méromorphe de la matrice de scattering pour des problèmes à deux corps à longue portée

Prolongement méromorphe de la matrice de scattering pour des problèmes à deux corps à longue portée

Propagation des mesures de Wigner à travers un croisement de codimension 1 dégénéré

Propagation of analytic singularities for the Schrödinger Equation

Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation

Propagation of singularities in many-body scattering in the presence of bound states

Puits multiples (d'après des travaux avec B. Helffer)

Puits multiples en limite semi-classique. II. Interaction moléculaire. Symétries. Perturbation

Puits multiples en mécanique semi-classique VI. (Cas des puits sous-variétés)

Currently displaying 21 – 30 of 30