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

Abstract

The Landauer conductance of a two terminal device equals to the number of open modes in the weak scattering limit. What is the corresponding result if we close the system into a ring? Is it still bounded by the number of open modes? Or is it unbounded as in the semi-classical (Drude) analysis? It turns out that the calculation of the mesoscopic conductance is similar to solving a percolation problem. The "percolation" is in energy space rather than in real space. The non-universal structures and the sparsity of the perturbation matrix cannot be ignored.

arXiv comment7 pages, 8 figures, with the correct version of Figs.6-7

References in corpus (6)

• Dynamic response of isolated Aharonov-Bohm rings coupled to an electromagnetic resonator
• Quantum pumping in closed systems, adiabatic transport, and the Kubo formula
• Classical and quantum pumping in closed systems
• Semilinear Response
• Rate of energy absorption by a closed ballistic ring
• The Multimode Conductance Formula for a Closed Ring

Cited by in corpus (6)

• Semilinear response for the heating rate of cold atoms in vibrating traps
• The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture
• Random-matrix modeling of semi-linear response, the generalized variable range hopping picture, and the conductance of mesoscopic rings
• From the Kubo formula to variable range hopping
• Diffusion in sparse networks: linear to semi-linear crossover
• Energy absorption by "sparse" systems: beyond linear response theory