The conductance of a multi-mode closed ballistic ring: Beyond Landauer and Kubo
S. Bandopadhyay, Y. Etzioni, and D. Cohen. 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.
%0 Book Section
%1 statphys23_0757
%A Bandopadhyay, S.
%A Etzioni, Y.
%A Cohen, D.
%B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics
%C Genova, Italy
%D 2007
%E Pietronero, Luciano
%E Loreto, Vittorio
%E Zapperi, Stefano
%K ballistic closed conductance device mesoscopic ring statphys23 topic-8
%T The conductance of a multi-mode closed ballistic ring: Beyond Landauer and Kubo
%U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=757
%X 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.
@incollection{statphys23_0757,
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.},
added-at = {2007-06-20T10:16:09.000+0200},
address = {Genova, Italy},
author = {Bandopadhyay, S. and Etzioni, Y. and Cohen, D.},
biburl = {https://www.bibsonomy.org/bibtex/2ef372056d6c28782a7a215d03af4343f/statphys23},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano},
interhash = {def75c2cc8c2726bbafbcd7f6fea0a34},
intrahash = {ef372056d6c28782a7a215d03af4343f},
keywords = {ballistic closed conductance device mesoscopic ring statphys23 topic-8},
month = {9-13 July},
timestamp = {2007-06-20T10:16:28.000+0200},
title = {The conductance of a multi-mode closed ballistic ring: Beyond Landauer and Kubo},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=757},
year = 2007
}