Time-dependent quantum transport: A practical scheme using density   functional theory
  We present a computationally tractable scheme of time-dependent transport phenomena within open-boundary time-dependent density-functional-theory. Within this approach all the response properties of a system are determined from the time-propagation of the set of ``occupied'' Kohn-Sham orbitals under the influence of the external bias. This central idea is combined with an open-boundary description of the geometry of the system that is divided into three regions: left/right leads and the device region (``real simulation region''). We have derived a general scheme to extract the set of initial states in the device region that will be propagated in time with proper transparent boundary-condition at the device/lead interface. This is possible due to a new modified Crank-Nicholson algorithm that allows an efficient time-propagation of open quantum systems. We illustrate the method in one-dimensional model systems as a first step towards a full first-principles implementation. In particular we show how a stationary current develops in the system independent of the transient-current history upon application of the bias. The present work is ideally suited to study ac transport and photon-induced charge-injection. Although the implementation has been done assuming clamped ions, we discuss how it can be extended to include dissipation due to electron-phonon coupling through the combined simulation of the electron-ion dynamics as well as electron-electron correlations. 
S. Kurth, G. Stefanucci, C.-O. Almbladh, A. Rubio, E.K.U. Gross