Quantum electron transport beyond linear response

After a brief historical survey and summary of previous work involving the linear response theory (LRT) Hamiltonian, H=H(system)−AF(t), where the latter part refers to the effect of an applied field F(t) as in Kubo's theory, we deal with the nonlinear problem in which the applied electric field of arbitrary strength, as well as a possible magnetic field, are included in the system Hamiltonian, H=H[system(E,B)]. In Part A of this study we deal with the general formalism on the many-body level. Projection operators are applied to the Von Neumann equation in the interaction picture, H(system)=H0+λV, which after the Van Hove limit, λ→0,t→∞,λ2tfinite, leads to the master equation for ∂ρ/∂t, containing both the Pauli–Van Hove diagonal part involving the transitions Wγγ′, and a nondiagonal quantum-interference part, as obtained by us previously. Likewise, the full many-body current operator JA is obtained by manipulation of the Heisenberg equation of motion for dA/dt in the interaction picture.