  The eigenvalues of the transmission matrix provide the basis for a full
description of the statistics of steady-state transmission and conductance. At
the same time, the ability to excite the sample with the waveform of specific
transmission eigenchannels allows for control over transmission. However, the
nature of pulsed transmission of transmission eigenchannels and their spectral
correlation, which would permit control of propagation in the time domain, has
not been discussed. Here we report the dramatic variation of the dynamic
properties of transmission with incident waveform. Computer simulations show
that lower-transmission eigenchannels respond more promptly to an incident
pulse and are correlated over a wide frequency range. We explain these results
together with the puzzlingly large dynamic range of transmission eigenvalues in
terms of the way quasi-normal modes of the medium combine to form specific
transmission eigenchannels. Key factors are the closeness of the illuminating
waves to resonance with the modes comprising an eigenchannel, their spectral
range, and the interference between the modes. We demonstrate in microwave
experiments that the modal characteristics of eigenchannels provide the optimum
way efficiently excite specific modes of the medium.
