The mesoscopic conductance of ballistic rings

TL;DR

This paper develops a theory for the conductance of ballistic rings in mesoscopic regimes, emphasizing the importance of energy-space percolation and non-universal quantum structures, which differ from classical expectations.

Contribution

It introduces a novel approach to calculate mesoscopic conductance by modeling it as an energy-space percolation problem, accounting for quantum non-ergodicity.

Findings

Conductance is significantly reduced compared to classical predictions.

Energy absorption depends on connected transition sequences in energy space.

Quantum non-ergodicity influences conductance in ballistic rings.

Abstract

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.