  We investigate the dephasing of mesoscopic interferences by electron-electron
interactions in a strictly one-dimensional geometry composed of two
weakly-coupled (clean and very long) Luttinger liquids. The main goal of this
paper is to demonstrate that interactions in one dimension can produce a
visible attenuation of Aharonov-Bohm oscillations. Through a Nyquist noise type
description of the interactions and a direct (exact) calculation based on the
Luttinger theory, in our setup we firmly emphasize that the dephasing time
results from the electron fractionalization time.
