Spectral and scattering theory for the Aharonov-Bohm operators

Konstantin Pankrashkin (1) , Serge Richard (2, 3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 ICJ - Institut Camille Jordan
3 DPMMS - Department of Pure Mathematics and Mathematical Statistics

We review the spectral and the scattering theory for the Aharonov-Bohm model on $\mathbb{R}^2$. New formulae for the wave operators and for the scattering operator are presented. The asymptotics at high and at low energy of the scattering operator are computed.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Konstantin Pankrashkin, Serge Richard. Spectral and scattering theory for the Aharonov-Bohm operators. Reviews in Mathematical Physics, 2011, 23, pp.53 - 81. ⟨hal-00436006⟩