Regensburg 2016 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 19: Transport: Fluctuation and Noise
(Joint session of DY and TT organized by TT)
DY 19.2: Vortrag
Dienstag, 8. März 2016, 14:15–14:30, H23
Statistics of transmission eigenvalues in diffusive star-shaped multi-terminal structures — Sven Essert, Viktor Krueckl, and •Klaus Richter — Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
We study transport in diffusive star-shaped devices with more than two leads. We find that the eigenvalue distribution p(t) of the transmission matrix between any pair of terminals is typically not showing the bimodal distribution that is found in two-lead devices. Instead, the distribution displays a cutoff tc, i. e., p(t)=0 for 1≥ t≥ tc. We explain the origin of this cutoff by deriving analytical expressions in the limit of low transmission for fully symmetric stars and for some limiting cases of extreme asymmetry. Using numerical calculations we probe the validity of these results away from the low-transmission limit.
In addition, we note that the bimodal distribution can be recovered when combining the leads of the star into meta leads in such a way that the total number of such meta leads is two. Then the transport between these is again bimodal, thus showing "open channels" with transmissions close to 1. Related to this, we propose the study of a new observable, which we call eigenvector splitting, that quantifies the distribution of outgoing flux among the constituent leads of the meta lead. This quantity becomes particularly interesting, when studying devices in the low-transmission limit, where it directly relates to the eigenvalue distribution. We present analytical solutions for the eigenvector splitting in some limiting geometries and supplement them by numerical calculations.