# Voltage fluctuations in mesoscopic metal rings and wires

## Abstract

We apply a recently developed multiterminal formalism to compute the fluctuations in the transport properties of mesoscopic rings. The voltage fluctuations V are not symmetric with respect to reversal of the magnetic field H. Contributions to the part of V symmetric with respect to reversal of H come from the whole length of the sample, while the antisymmetric part of V comes only from the region of the junction between the voltage and current leads. We show that the Aharonov-Bohm (AB) oscillation decreases exponentially with Cring/Lin (Cring denotes the circumference of the ring, Lin denotes the inelastic mean free path). The AB oscillations in the voltage are not symmetric with respect to zero H fieldin the highly coherent regime (Cring/Lin<1) the phase of this oscillation can take on any value, while in the classical limit the phase becomes symmetric0 or . We demonstrate the existence of nonlocal voltage fluctuations, ones in which the current path and voltage path do not intersect; both aperiodic fluctuations and AB oscillations fall off exponentially with d/Lin, where d is the closest approach of the current and voltage paths. Finally, we obtain new results on the energy correlation Ec for the AB effect, finding it to be larger than previously expected. © 1988 The American Physical Society.