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arXiv · 1111.1706

Transmission eigenvalues and the bare conductance in the crossover to Anderson localization

Zhou Shi·Azriel Z. Genack
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Abstract

We measure the field transmission matrix t for microwave radiation propagating through random waveguides in the crossover to Anderson localization. From these measurements, we determine the dimensionless conductance, g, and the individual eigenvalues $τ_n$ of the transmission matrix $tt^\dagger$ whose sum equals g. In diffusive samples, the highest eigenvalue, $τ_1$, is close to unity corresponding to a transmission of nearly 100%, while for localized waves, the average of $τ_1$, is nearly equal to g. We find that the spacing between average values of $\lnτ_n$ is constant and demonstrate that when surface interactions are taken into account it is equal to the inverse of the bare conductance.

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Zhou Shi, Azriel Z. Genack. 2012-01-09. Transmission eigenvalues and the bare conductance in the crossover to Anderson localization. https://doi.org/10.1103/physrevlett.108.043901

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