Inverse scattering at high energies for a classical particle in a long range force field

Alexandre Jollivet (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We define scattering data for the Newton equation in an electromagnetic field $(-\nabla V,B)\in C^1(\R^n,\R^n)\times C^1(\R^n,A_n(\R))$, $n\ge 2$, that decay at infinity like $r^{-\alpha-1}$ for some $\alpha\in (0,1]$, where $A_n(\R)$ is the space of $n\times n$ antisymmetric matrices. We provide their high energies asymptotics and we prove, in particular, that the scattering data at high energies uniquely determine the short range part of $(\nabla V,B)$ up to the knowledge of the long range part of $(\nabla V,B)$. Other asymptotic regimes are also considered. This paper extends similar results for a short range force field [Jollivet, 2009] or for a long range electric (or gravitational) field [Jollivet, 2013].

Mots clés: Newton equation; Long range electromagnetic field; Inverse scattering at high energies

Domaines: Physique mathématique [math-ph]

Alexandre Jollivet. Inverse scattering at high energies for a classical particle in a long range force field. 2014. ⟨hal-01063458v2⟩