Mesoscopic decoherence in Aharonov-Bohm rings

We study electron decoherence by measuring the temperature dependence of Aharonov-Bohm (AB) oscillations in quasi-1D rings, etched in a high-mobility GaAs/GaAlAs heterostructure. The oscillation amplitude is influenced both by phase-breaking and by thermal averaging. Thermal averaging is important when the temperature approaches the energy scale, on which the AB oscillations shift their phase. For the phase-breaking, it is demonstrated that the damping of the oscillation amplitude is proportional to the length of the interfering paths. For temperatures $T$ from 0.3 to 4 $\rm K$ we find the phase coherence length $\it L_{\phi}$ $\propto$ $T^{-1}$, close to what has been reported for open quantum dots. This might indicate that the $T^{-1}$ decoherence rate is a general property of open and ballistic mesoscopic systems.