Giant fluctuations of topological charge in a disordered wave guide

We study the fluctuations of the total topological charge of a scalar wave propagating in a hollow conducting wave guide filled with scatterers inside. We investigate the dependence of the screening on the scattering mean free path and on the presence of boundaries. Near the cut-off frequencies of the wave guide, screening is strongly suppressed near the boundaries. The resulting huge fluctuations of the total topological charge are very sensitive to the disorder.