Аннотация
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.
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