Abstract
This chapter describes the ab initio theory of quantum transport. The Cini scheme can be combined with time-dependent density functional theory (TDDFT). In this theory, the time-dependent density of an interacting system moving in an external, time-dependent local potential can be calculated via a fictitious system of non-interacting electrons moving in a local, effective, and time-dependent potential. Therefore this theory is well suited for the treatment of non-equilibrium transport problems. The steady-state approach based on DFT, exchange, and correlation is approximated by the static Kohn–Sham (KS) potential and the charge density is obtained self-consistently in the presence of the steady current. The TDDFT formulation, as opposed to the static DFT formulation, is thermodynamically consistent and is not limited to the steady-state regime. Also, it has the extra merit of accessing the true excitation energies of interacting systems. The chapter also provides an elementary introduction to the Keldysh contour, the Keldysh–Green functions, and the Keldysh book-keeping.
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