Joshi Krishna, Kurtz Israel, Shi Zhou, Genack Azriel Z
Department of Physics, Queens College of the City University of New York, Flushing, New York, 11367, USA.
Physics Program, The Graduate Center of the City University of New York, New York, New York, 10016, USA.
Nat Commun. 2024 Dec 5;15(1):10616. doi: 10.1038/s41467-024-54012-8.
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.
量子电导及其经典波动类似物——透射率，由传输矩阵的本征值之和给出。然而，尚未对传输本征通道进行测量或理论分析，以解释在引入新通道时模拟中发现的电导下降现象。在此，我们测量了随机波导的微波传输矩阵，并找到了所有传输本征值的谱，即使是在最低传输本征通道中的下降处，其幅度比传输矩阵中的噪声低几个数量级。在拓扑传输零点处（样品输出处的能量密度消失）以及在向新通道的交叉处（纵向速度消失），传输都会消失。传输零点会拉低所有传输本征值，从而在透射率中产生下降。这些下降以及探测甚至最低传输本征通道特性的能力是由于本征值之间的相关性。态密度峰值对电导下降的精确跟踪表明传输矩阵的零点和极点之间存在进一步的相关性。随着样品宽度根据对应原理增加，电导趋近于欧姆定律。
