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Abstract The quantum conductance and its classical wave analogue, the transmittance, are given by the sum of the eigenvalues of the transmission matrix. However, neither measurements nor theoretical analysis of the transmission eigenchannels have been carried out to explain the dips in conductance found in simulations as new channels are introduced. Here, we measure the microwave transmission matrices of random waveguides and find the spectra of all transmission eigenvalues, even at dips in the lowest transmission eigenchannel that are orders of magnitude below the noise in the transmission matrix. Transmission vanishes both at topological transmission zeros, where the energy density at the sample output vanishes, and at crossovers to new channels, where the longitudinal velocity vanishes. Zeros of transmission pull down all the transmission eigenvalues and thereby produce dips in the transmittance. These dips and the ability to probe the characteristics of even the lowest transmission eigenchannel are due to correlation among the eigenvalues. The precise tracking of dips in the conductance by peaks in the density of states points to a further correlation between zeros and poles of the transmission matrix. The conductance approaches Ohm’s law as the sample width increases in accord with the correspondence principle.
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Velocities of transmission eigenchannels and diffusion
Abstract The diffusion model is used to calculate both the time-averaged flow of particles in stochastic media and the propagation of waves averaged over ensembles of disordered static configurations. For classical waves exciting static disordered samples, such as a layer of paint or a tissue sample, the flux transmitted through the sample may be dramatically enhanced or suppressed relative to predictions of diffusion theory when the sample is excited by a waveform corresponding to a transmission eigenchannel. Even so, it is widely assumed that the velocity of waves is irretrievably randomized in scattering media. Here we demonstrate in microwave measurements and numerical simulations that the statistics of velocity of different transmission eigenchannels are distinct and remains so on all length scales and are identical on the incident and output surfaces. The interplay between eigenchannel velocities and transmission eigenvalues determines the energy density within the medium, the diffusion coefficient, and the dynamics of propagation. The diffusion coefficient and all scattering parameters, including the scattering mean free path, oscillate with the width of the sample as the number and shape of the propagating channels in the medium change.
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- Award ID(s):
- 2211646
- PAR ID:
- 10496641
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Nature Communications
- Volume:
- 15
- Issue:
- 1
- ISSN:
- 2041-1723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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