An amplitude-phase (Ermakov-Lewis) approach for the Jackiw-Pi model of bilayer graphene

Abstract

In the context of bilayer graphene we use the simple gauge model of Jackiw and Pi to construct its numerical solutions in powers of the bias potential V according to a general scheme due to Kravchenko. Next, using this numerical solutions, we develop the Ermakov-Lewis approach for the same model. This leads us to numerical calculations of the Lewis-Riesenfeld phases that could be of forthcoming experimental interest for bilayer graphene. We also present a generalization of the Ioffe-Korsch nonlinear Darboux transformation