Nodal domains in open microwave systems

Abstract

Nodal domains are studied both for real ${\psi }_R$ and imaginary part ${\psi }_I$ 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 ${\varphi }_g$ according to ${\psi }_R+i{\psi }_I=e^{i{\varphi }_g}({\psi }_R^{\prime }+i{\psi }_I^{\prime })$. This variation can be qualitatively, and the correlation quantitatively explained in terms of the phase rigidity characterising the openness of the billiard.

7 pages, 10 figures, submitted to PRE

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• On the theory of cavities with point-like perturbations. Part I: General theory
• Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance
• Local Weak Limits of Laplace Eigenfunctions
• A difference-equation formalism for the nodal domains of separable billiards
• On the Nodal Count Statistics for Separable Systems in any Dimension