Nodal domains in open microwave systems

TL;DR

This paper investigates the properties of nodal domains in open microwave systems, revealing their similarities to closed systems and analyzing how phase variations affect nodal domain characteristics.

Contribution

It introduces an analysis of nodal domains in open microwave cavities and explains phase variation effects using phase rigidity, a novel approach for such systems.

Findings

Nodal domains in open systems behave similarly to those in closed billiards.

Phase variation affects the number and correlation of nodal domains.

Phase rigidity explains the observed phase-dependent behavior.

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 $\phi_g$ according to $\psi_R+i\psi_I=e^{i\phi_g}(\psi_R'+i\psi_I')$. This variation can be qualitatively, and the correlation quantitatively explained in terms of the phase rigidity characterising the openness of the billiard.