Time-dependent density functional theory for quantum transport

The rapid miniaturization of electronic devices motivates research interests in quantum transport. Recently time-dependent quantum transport has become an important research topic. Here we review recent progresses in the development of time-dependent density-functional theory for quantum transport including the theoretical foundation and numerical algorithms. In particular, the reduced-single electron density matrix based hierarchical equation of motion, which can be derived from Liouville-von Neumann equation, is reviewed in details. The numerical implementation is discussed and simulation results of realistic devices will be given.