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

Y.V. Fyodorova, b, M. Osmana aKing's College London, Department of Mathematics, London WC2R 2LS, United Kingdom bL.D. Landau Institute for Theoretical Physics, Semenova 1a, 142432 Chernogolovka, Russia

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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.

DOI:10.12693/APhysPolA.140.487 topics: coherent perfect absorption, non-hermitian random matrices, eigenvector non-orthogonality