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

Jollivet, Alexandre

Document type :

Pré-publication ou Document de travail

Title :

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

Author(s) :

Jollivet, Alexandre [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

Newton equation
Long range electromagnetic field
Inverse scattering at high energies

HAL domain(s) :

Mathématiques [math]/Physique mathématique [math-ph]

English abstract : [en]

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 $\alpha\in (0,1]$, ...
Show more >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].Show less >

Language :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

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