Exact solution of scattering on two Aharonov-Bohm vortices.

Eugène Bogomolny, LPTMS, CNRS, Paris XI University.

The effect of Aharonov-Bohm with one and  two vortices is briefly considered. It is demonstrated how a careful investigation of singularities around each vortex permits to reconstruct explicitly the full solution. In the end two-vortex wave function is expressed through a solution of the Painlevé III equation.