Quantum Oscillations and the Aharonov-Bohm Effect for Parallel Resistors

The transmission coefficient between two terminals of a one-dimensional ring with arbitrary scatterers is calculated exactly as a function of enclosed magnetic flux, $\ensuremath{\phi}$. At low temperatures, where the inelastic diffusion length is larger than the size of the ring, its conductance follows from the Landauer formula. Oscillations of the conductance as a function of the characteristics of the scatterers and of $\ensuremath{\phi}$ (with a period ${\ensuremath{\phi}}_{0}=\frac{\mathrm{hc}}{e}$) are found. The oscillations persist even when the elastic scattering is strong.

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