Can a local repulsive potential trap an electron?

Nils Berglund, Alex Hansen, Eivind H. Hauge and Jarosław Piasecki
Phys. Rev. Letters 77, 2149-2152 (1996)

We study the classical dynamics of a charged particle in two dimensions, under the influence of a perpendicular magnetic and an in-plane electric field. We prove the surprising fact that there is a finite region in phase space that corresponds to the otherwise drifting particle being trapped by a local repulsive potential. Our result is a direct consequence of KAM-theory and, in particular, of Moser's theorem. We illustrate it by numerical phase portraits and by an analytic approximation to invariant curves.

Keywords and phrases: billiards, KAM-theory, chaotic scattering, Lorentz model.

 

Journal Homepage Published article: 10.1103/PhysRevLett.77.2149

PDF file (148 Kb) hal-00130560 arXiv/chao-dyn/9604018