The mesoscopic conductance of ballistic rings
  The calculation of the conductance of ballistic rings requires a theory that goes well beyond the Kubo-Drude formula. Assuming "mesoscopic" circumstance of very weak environmental relaxation, the conductance is much smaller compared with 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 are implied by lack of quantum-chaos ergodicity in ring shaped ballistic devices. 
Yoav Etzioni, Swarnali Bandopadhyay, Doron Cohen