 
Summary: Dynamics of a classical Hall system driven
by a timedependent AharonovBohm flux
J. Ascha
CPTCNRS, Luminy Case 907, F13288 Marseille Cedex 9, France
P. Sovícek
Department of Mathematics, Faculty of Nuclear Science, Czech Technical University,
Trojanova 13, 120 00 Prague, Czech Republic
Received 4 September 2006; accepted 16 March 2007; published online 10 May 2007
We study the dynamics of a classical particle moving in a punctured plane under
the influence of a homogeneous magnetic field, an electric background, and driven
by a timedependent singular flux tube through the hole. We exhibit a striking
de localization effect: when the electric background is absent we prove that a
linearly timedependent flux tube opposite to the homogeneous flux eventually
leads to the usual classical Hall motion: the particle follows a cycloid whose center
is drifting orthogonal to the electric field; if the fluxes are additive, the drifting
center eventually gets pinned by the flux tube whereas the kinetic energy is grow
ing with the additional flux. © 2007 American Institute of Physics.
DOI: 10.1063/1.2723550
I. INTRODUCTION
The motivation to study the dynamics of this classical system is to sharpen our intuition on its
