Lecturer:  Azriel Z. Genack, Distinguished Professor, Queens College, City University of New York
 Abstract:
The quantum nature of electronic conductance is manifest in magnetoresistance fluctuations due to the interference of multiply scattered electronic waves at ultralow temperatures in micron- sized mesoscopic conductors, in which the wave is temporally coherent. Quantum transport is also seen in the stepwise increase in electronic conductance in ballistic heterojunctions with increasing width as new wave channels are introduced. Equivalent steps in ballistic optical transmittance are observed when an aperture is illuminated with diffuse light. Dips in the conductance have been found in simulations in diffusive media, but measurements of the conductance or the transmittance have not been performed despite the centrality of conductance in mesoscopic physics. Here we measure the microwave transmittance through random waveguides and find dips that arise due to the vanishing of transmission in an eigenchannel of the transmission matrix arising from two distinct effects: Either the energy density on the output surface vanishes as transmission zeros in the map of the phase of the determinant of the transmission matrix reach the real axis of the complex frequency plane before the crossover to a new channel, or the longitudinal velocity of a newly introduced transmission eigenchannel vanishes. Even though the transmission in the lowest transmission eigenchannel is exponentially small, correlation between the transmission eigenvalues pulls down the transmission of other eigenchannels, thereby affecting the conductance. The changing statistics of transmission zeros with sample dimensions determines both the departures from and the approach to Ohm’s law in mesoscopic conductors. The zero in eigenchannel velocity at the crossover to a new channel is reminiscent of the Wigner cusp anomaly in the nuclear scattering cross sections when a new channel is opened.