Stochastic mechanics of electron transfer in graphene

In this paper, we present a new approach to electron transports in nano-scale devices by using Nelson's quantum stochastic mechanical simulations. Transferring electrons in pure and doped graphene ribbons (GRs) are numerically investigated as quantum Brownian motions with wavefunctions of isolated GRs. The time evolution of the quantum stochastic process is given by Ito type stochastic differential equation. From the analysis of the electron motion, we directly obtain the electron mobilities in GRs under some electric fields. We show the electron motion depends on the stochastic distribution of the eigenfunction or the molecular orbital and then the electron mobility is affected by the dopant atom.