A model of dephasing in shift current processes

The shift current, a nonlinear effect, is thought to be an important transport mechanism in many ferroelectrics and to carry information about the geometry of the Bloch wave function. Contrary to standard transport processes, it depends on the off-diagonal elements of the density matrix and not on the occupation of energy levels. We construct a simple model of dissipation beyond the relaxation-time approximation for shift current processes for electrons in a one-dimensional chain of ions lacking inversion symmetry and coupled to external electric and magnetic fields. The model allows to study if and how the system reaches non-equilibrium steady states.