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Ohm’s law lost and regained: observation and impact of transmission and velocity zeros

Author

Listed:
  • Krishna Joshi

    (Flushing
    New York)

  • Israel Kurtz

    (Flushing
    New York)

  • Zhou Shi

    (Flushing
    New York
    19 School House Road)

  • Azriel Z. Genack

    (Flushing
    New York)

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.

Suggested Citation

  • Krishna Joshi & Israel Kurtz & Zhou Shi & Azriel Z. Genack, 2024. "Ohm’s law lost and regained: observation and impact of transmission and velocity zeros," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-54012-8
    DOI: 10.1038/s41467-024-54012-8
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    References listed on IDEAS

    as
    1. A. A. Chabanov & M. Stoytchev & A. Z. Genack, 2000. "Statistical signatures of photon localization," Nature, Nature, vol. 404(6780), pages 850-853, April.
    2. Tal Schwartz & Guy Bartal & Shmuel Fishman & Mordechai Segev, 2007. "Transport and Anderson localization in disordered two-dimensional photonic lattices," Nature, Nature, vol. 446(7131), pages 52-55, March.
    3. Azriel Z. Genack & Yiming Huang & Asher Maor & Zhou Shi, 2024. "Velocities of transmission eigenchannels and diffusion," Nature Communications, Nature, vol. 15(1), pages 1-10, December.
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