Power statistics for wave propagation in one dimension and comparison with radiative transport theory

We consider a one-dimensional medium with random index of refraction or a transmission line with random capacitance per unit length, allowing for impedance mismatch at the load and generator. We compute the expected value of the incident and reflected powers at any point between the generator and load in the limit of weak fluctuations and a long line. The results are compared with those of radiative transport theory and discrepancies show the limitations of that theory. Finally, we consider the spreading of pulses due to random fluctuations.