Transmission-eigenchannel velocity and diffusion

The diffusion model is used to calculate the time-averaged flow of particlesin stochastic media and the propagation of waves averaged over ensembles ofdisordered static configurations. For classical waves exciting staticdisordered samples, such as a layer of paint or a tissue sample, the fluxtransmitted through the sample may be dramatically enhanced or suppressedrelative to predictions of diffusion theory when the sample is excited by awaveform corresponding to a transmission eigenchannel. Even so, it is widelyacknowledged that the velocity of waves is irretrievably randomized inscattering media. Here we demonstrate in microwave measurements and numericalsimulations that the statistics of velocity of different transmissioneigenchannels remain distinct on all length scales and are identical on theincident and output surfaces. The interplay between eigenchannel velocities andtransmission eigenvalues determines the energy density within the medium, thediffusion coefficient, and the dynamics of propagation. the diffusioncoefficient and all scatter9ng parameters, including the scattering mean freepath, oscillate with width of the sample as the number and shape of thepropagating channels in the medium change.