  We discuss the concept of the Berry phase in a dissipative system. We show
that one can identify a Berry phase in a weakly-dissipative system and find the
respective correction to this quantity, induced by the environment. This
correction is expressed in terms of the symmetrized noise power and is
therefore insensitive to the nature of the noise representing the environment,
namely whether it is classical or quantum mechanical. It is only the spectrum
of the noise which counts. We analyze a model of a spin-half (qubit)
anisotropically coupled to its environment and explicitly show the coincidence
between the effect of a quantum environment and a classical one.
