Nodal domains in open microwave systems

Nodal domains are studied both for real psiR and imaginary part psiI of the wave functions of an open microwave cavity and found to show the same behavior as wave functions 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 phig according to psiR+ipsiI=eiphig(psiR'+ipsiI'). This variation can be qualitatively, and the correlation quantitatively explained in terms of the phase rigidity characterizing the openness of the billiard.