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Nodal domains in open microwave systems

Nodal domains are studied both for real $ψ_R$ and imaginary part $ψ_I$ of the wavefunctions of an open microwave cavity and found to show the same behavior as wavefunctions in closed billiards. In addition we investigate the variation of the number of nodal domains and the signed area correlation by changing the global phase $ϕ_g$ according to $ψ_R+iψ_I=e^{iϕ_g}(ψ_R'+iψ_I')$. This variation can be qualitatively, and the correlation quantitatively explained in terms of the phase rigidity characterising the openness of the billiard.