Numerical study of the distribution of phase as an electron moves in a one-dimensional, continuously and randomly varying potential

In this paper the authors study the phase distribution of the wavefunction of an electron as it moves through a one-dimensional continuously and randomly varying potential. The authors note that in the mesoscopic region where the reflectance fluctuates and depends crucially on the boundary conditions, the phase distribution is always peaked and non-stationary. However, in the asymptotic region, which depends on the degree of disorder, for weak disorders, the phase distribution becomes uniform. However, for strong disorders, the phase distribution becomes stationary and peaked. This leads to phase pinning