Our previous results on the nonperturbative calculations of the mean current and of the energy-momentum tensor in QED with the $T$-constant electric field are generalized to arbitrary dimensions. The renormalized mean values are found, and the vacuum polarization contributions and particle creation contributions to these mean values are isolated in the large $T$ limit; we also relate the vacuum polarization contributions to the one-loop effective Euler-Heisenberg Lagrangian. Peculiarities in odd dimensions are considered in detail. We adapt general results obtained in $2+1$ dimensions to the conditions which are realized in the Dirac model for graphene. We study the quantum electronic and energy transport in the graphene at low carrier density and low temperatures when quantum interference effects are important. Our description of the quantum transport in the graphene is based on the so-called generalized Furry picture in QED where the strong external field is taken into account nonperturbatively; this approach is not restricted to a semiclassical approximation for carriers and does not use any statistical assumptions inherent in the Boltzmann transport theory. In addition, we consider the evolution of the mean electromagnetic field in the graphene, taking into account the backreaction of the matter field to the applied external field. We find solutions of the corresponding Dirac-Maxwell set of equations and with their help we calculate the effective mean electromagnetic field and effective mean values of the current and the energy-momentum tensor. The nonlinear and linear $I\mathrm{\text{−}}V$ characteristics experimentally observed in both low- and high-mobility graphene samples are quite well explained in the framework of the proposed approach, their peculiarities being essentially due to the carrier creation from the vacuum by the applied electric field.

• Received 6 July 2012

DOI:https://doi.org/10.1103/PhysRevD.86.125022