Eigenfunction Non-Orthogonality in Open Wave Chaotic Systems: Non-Perturbative RMT Results for Single-Channel Scattering

We present explicit distributions of diagonal non-orthogonality overlaps (also known as the Petermann factors) characterizing eigenmodes in a wave-chaotic cavity open via a single decay channel. We show that such factors should determine the shape of deep dips in the wave reflection experiments. The explicit distributions of the Petermann factors valid for an arbitrary strength of coupling to the scattering channel are obtained within the random matrix theory framework. The regime of weak-coupling allows further simplifications.

Automated summary

This study presents explicit distributions of diagonal non-orthogonality overlaps, also known as Petermann factors, characterizing eigenmodes in a wave-chaotic cavity. It shows that these factors determine deep dips in wave reflection experiments and are valid for arbitrary coupling strengths within the framework of random matrix theory. Further simplifications are possible in the regime of weak coupling.