Incollection,

The conductance of a multi-mode closed ballistic ring: Beyond Landauer and Kubo

, , and .
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)

Abstract

The calculation of the conductance of closed ballistic rings requires a theory that goes well beyond the Kubo-Drude formula S. Bandopadhyay, Y. Etzioni and D. Cohen, Europhys. Lett. 76, 739 (2006). To realise the ballistic case we use a single scatterer, characterised by the total transmission $g_T$, in the ring. Assuming mesoscopic circumstances of very weak environmental relaxation, the conductance is much smaller compared to the naive expectation. Namely, the electro-motive force induces an energy absorption with a rate that depends crucially on the possibility to make connected sequences of transitions. Thus the calculation of the mesoscopic conductance is similar to solving a percolation problem. The percolation is in energy space rather than in real space. Non-universal structures and sparsity of the perturbation matrix cannot be ignored. The latter is implied by a lack of quantum-chaos ergodicity in ring shaped ballistic devices. Our study also distinguish between the initial transient response (spectroscopic conductance) and the long-time steady state response (mesoscopic conductance) Y. Etzioni, S. Bandopadhyay and D. Cohen, cond-mat/0607746. The mesoscopic conductance may be larger than Landauer conductance depending on number of open modes $M$ and the level-broadening parameter $\gamma$. This way, our study goes beyond Landauer.

Tags

Users

  • @statphys23

Comments and Reviews