Abstract: Time-dependent quantum transport (TDQT) theory researches the electron wave evolution in the open systems. Due to the dissipation of leads or other environmental effects, the electrons behavior in the central region does not only depends on the instant external fields, but also on the historical accumulations in some past period. This is a non-Markov process, which is some complicated to be solved in mathematics. In this paper, we introduce a new type of TDQT theory: density-matrix equation of motion (DM-EOM) method in detail. It is based on the non-equilibrium Green’s function (NEGF) theory. This method has clear calculation schemes and it is easy for the numerical implementation, especially for the large systems. We also introduce some other QDTD methods and their applications. For example, the transient current in graphene and other 2D materials, the electron dynamics in open quantum dots with the many-body interactions.

Key words: quantum transport; time-dependent; equation of motion; non-equilibrium Green’s function theory; complex absorbing potential; self-energy