Transmission of particles through a random one-dimensional potential

Abstract

The transmission of a particle through a random chain of delta functions is studied both numerically and analytically. Several statistical ensembles were used. The results show that the logarithm of the transmission coefficient obeys the central-limit theorem and its average scales linearly with the length of the system. The averages of the transmission coefficient and its inverse show ensemble-independent behavior only in the weak-scattering limit. They scale exponentially with different characteristic lengths, which are related to the average of the logarithm of the transmission coefficient. In the strong-scattering limit the averages of the transmission coefficient and its inverse depend strongly on the statistical ensemble used, thus indicating that they are not physically meaningful quantities. DOI: http://dx.doi.org/10.1103/PhysRevB.24.1761 © 1981 The American Physical Society