  The quantum conductance and its classical wave analogue, the transmittance,
are given by the sum of the eigenvalues of the transmission matrix. The lowest
transmission eigenvalue in diffusive media might be expected to play a
negligible role in the conductance, and, in any case, to be too small to be
observed. Here, we observe the lowest transmission eigenchannel in microwave
waveguides, though it is orders of magnitude below the nominal noise level, and
show that the transmittance is pulled down by global correlation among
transmission eigenvalues and among zeros and poles of the transmission matrix.
Transmission vanishes either when the energy density on the sample output
vanishes at topological transmission zeros or when the longitudinal velocity
vanishes precisely at the crossover to a new channel. This lowers the
conductance by an amount proportional to the modulation of the density of
states. In accord with the correspondence principle, the conductance approaches
Ohms law as the number of channels increases with sample width. The exploration
of the transmission matrix opens the door to a new understanding of mesoscopic
transport and ultrasensitive detection techniques.
