The R-Σ Approach to Tunnelling in Nanoscale Devices

The R-Σ method provides the time evolution of two dynamical variables extracted from a wave function, namely, the expectation value of the position and the dispersion. It overcomes the Ehrenfest approximation while keeping the Newtonian form of the equations, thus providing the basis for including quantum features into the description of the single-particle dynamics and for extending such features to the collective-transport case. Here the single-particle R-Σ equations are applied to the case of tunnelling, and the results are compared with a full-quantum calculation.