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

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

2011-11-07

arxiv.org/abs/1111.1706v5

Phys. Rev. Lett. 108, 043901 (2012)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.108.043901

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 $\tau_n$ of the transmission matrix $tt^\dagger$ whose sum equals g. In diffusive samples, the highest eigenvalue, $\tau_1$, is close to unity corresponding to a transmission of nearly 100%, while for localized waves, the average of $\tau_1$, is nearly equal to g. We find that the spacing between average values of $\ln\tau_n$ 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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