  We study the robustness of geometric phase in the presence of parametric
noise. For that purpose we consider a simple case study, namely a semiclassical
particle which moves adiabatically along a closed loop in a static magnetic
field acquiring the Dirac phase. Parametric noise comes from the interaction
with a classical environment which adds a Brownian component to the path
followed by the particle. After defining a gauge invariant Dirac phase, we
discuss the first and second moments of the distribution of the Dirac phase
angle coming from the noisy trajectory.
