Relation between nonequilibrium Green’s function and Lippmann-Schwinger formalism in the first-principles quantum transport theory

In first-principles theory of nonequilibrium quantum transport, there are two main formalisms---the nonequilibrium Green's function (NEGF) and the Lippmann-Schwinger (LS) equation, which have been applied to a wide range of device physics problems when coupled with electronic structure methods such as the density-functional theory. In this work, we derive a relationship that formally connects the two formalisms at nonequilibrium. The relation is between the nonequilibrium scattering wave function and NEGF and it cannot be derived directly from the LS equation itself. We also found that the relation is practically useful by giving rise to a significant speed up in numerical computation of transmission coefficients for multiprobe systems.