Robustness Of The Geometric Phase Under Parametric Noise

We study the robustness of the geometric phase in the presence of parametric noise. For this purpose we consider a simple case study, namely a semiclassical particle that 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.