Nonequilibrium linked cluster expansion for steady-state quantum transport

We generalize the linked cluster expansion of Matsubara Green functions into nonequilibrium situations. This allows us to compute nonequilibrium correlation functions and, consequently, physical observables for interacting quantum systems with intermediate interaction strengths. As a specific example, we study nonlinear dc transport in a resonant tunneling system with electron-phonon interaction. The firstand second-order nonequilibrium cluster approximations are explicitly evaluated. The results are compared with those obtained by the standard nonequilibrium Green functions approach within the Migdal approximation for the self-energy and in the low-density limit also with the known exact solution. For moderately strong electron-phonon interactions the first-order linked cluster approximation is more precise than the Migdal approach. The secondorder approximation appears to be problematic in the presence of the Fermi sea. @S0163-1829~97!02435-1#