Monte Carle simulation of quantum transport through nanostructures

We describe a numerical scheme of combining Monte Carlo procedure and quantum scattering theory to simulate electron transport processes through nanostructures. The transport of electrons through a nanostructure is a highly nontrivial nonequilibrium process in which we should consider the interplay of (i) complicated many-body quantum states in nanostructure, (ii) thermal relaxation processes keeping the leads (electron reservoirs) in local equilibrium, (iii) the coupling between the leads and the nanostructure, and (iv) the bias causing nonequilibrium, current, and evolution of quantum states in the nanostructure. Considering the quantum coherence within the nanostructure, we include the degrees of freedom of the nanostructure and a single tunneling electron and solve the Schrِdinger equation for the many-body states to obtain the scattering matrix in the Fock space from which both the transmission of the electron and the variation of the states in nanostructure can be full quantum-mechanically calculated. The transport is investigated by the Monte Carlo simulation of successive scattering events of single electrons which are sampled with the Metropolis scheme governed by the scattering probabilities, the thermal statistics in the leads, and the applied bias. By this way from a given initial nanostructure state we can calculate the time evolutions of the current and the internal state. As examples we investigate the transmission of electrons through a two-level system. It is shown that the proposed method can properly deal with the inelastic effects in transport processes.