Dynamical approach to ballistic transport in graphene

The process of the coherent creation of particle-hole excitations by an electric field in graphene is quantitatively described beyond linear response. We calculate the evolution of the current density and the number of pairs in the ballistic regime using the tight binding model. While for small electric fields the I-V curve is linear characterized by the universal minimal resistivity σ=π/2(e2/h), for larger fields, after a certain time interval, the linear regime crosses over to a quadratic one and finally at larger times Bloch oscillations set in.