Magnetoresistance Fluctuations in Mesoscopic Wires and Rings

A simulation of the magnetoresistance of very small wires shows sample-specific, aperiodic structure due to the non-self-averaging nature of quasi-one-dimensional conductors in this size range. This explains earlier failures to observe flux-periodic magnetoresistance in very small rings. Analysis of the temperature and size dependence of the effect gives good agreement with experiment. A prediction is made for the experimental conditions in which oscillations periodic with flux $\frac{\mathrm{hc}}{e}$ will be observed.