  The amplitude of the Bohm-Aharonov oscillations of a particle moving around a
ring threaded by a magnetic flux and coupled to different dissipative
environments is studied. The decay of the oscillations when increasing the
radius of the ring is shown to depend on the spatial features of the coupling.
When the environment is modelled by the Caldeira-Leggett bath of oscillators,
or the particle is coupled by the Coulomb potential to a dirty electron gas,
interference effects are suppressed beyond a finite length, even at zero
temperature. A finite renormalization of the Aharonov-Bohm oscillations is
found for other models of the environment.
