Particle transport in a disordered medium: Numerical experiment

Using the multicenter Schrödinger equation for calculating the transmittance of a flat layer of randomly distributed point scattering centers through which a particle passes, we show that when the scattering length for one center is comparable to the particle wavelength λ or is larger, the Ioffe-Regel hypothesis holds. (According to this hypothesis, as the scatterer number density increases, the transmittance of the layer becomes constant, while the value of the particle’s effective mean free path remains of order λ.) When the scattering length is small compared to λ, the Ioffe-Regel hypothesis does not hold. As the scattering length decreases, the accuracy of the approximation of the effective scattering potential gradually increases, and, depending on the strength of the potential, particles may either tunnel or diffuse; the effective mean free path can be much smaller than λ.