Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: Exact calculation based on the invariant imbedding method

Abstract

We revisit the problem of disorder-enhanced tunneling transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension. Using the invariant imbedding theory of wave propagation generalized to randomly stratified media, we calculate the disorder-averaged logarithmic transmittance in the thick barrier limit and the disorder-averaged transmittance in a numerically exact manner. We confirm that the tunneling decay length obtained from the mean logarithmic transmittance behaves nonmonotonically as a function of the disorder strength and takes its maximum value at some finite value of the disorder parameter. We find that this nonmonotonic dependence persists in the presence of weak inelastic scattering inside the tunneling barrier. When the system size is larger than some critical value, which is somewhat smaller than the wavelength of the incident matter wave, we observe that the disorder-averaged transmittance also shows a similar nonmonotonic dependence on the disorder strength. In other words, weak disorder enhances the transmission, while strong disorder suppresses it. When the system size is smaller than the critical value, the disorder-averaged transmittance decreases monotonically as the disorder strength increases