Time-dependent quantum transport in the presence of elastic scattering

Abstract

Abstract A time-dependent quantum transport model considering elastic scattering is proposed. The model, solves the time-dependent Schrodinger equation in the presence of scattering. Inspired by the non-equilibrium Green's function (NEGF) method, an imaginary potential is added to the time-dependent Schrodinger equation for absorbing electron waves and a source term to model the injection of electron waves. The value of the imaginary potential is chosen so that the total probability density of the waves is conserved. A perfect absorber boundary condition is used to prevent wave reflection from boundaries in all the simulations. To verify the accuracy of the model, the results are compared with those of other methods in different scenarios. In a simple scenario where the quantum effects are not so significant, our results are close to those obtained from Boltzmann transport equation. In another scenario which uses a potential profile like a resonant tunneling diode, the results in the steady-state conditions are close to those obtained from NEGF method in self-consistent Born approximation. Moreover, the transmission chart for a resonant structure in the steady-state conditions shows that decoherence is well included in the proposed model.