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Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities

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Original languageEnglish
Article number224013
JournalJournal of Physics A: Mathematical and Theoretical
Issue number22
Published7 Jun 2022

Bibliographical note

Funding Information: This article is dedicated to the memory of Fritz Haake, whose influential paper [] was arguably the first addressing the statistics of S-matrix poles non-perturbatively within random matrix theory. YVF acknowledges financial support from EPSRC Grant EP/V002473/1 ‘Random Hessians and Jacobians: theory and applications’. Publisher Copyright: © 2022 The Author(s). Published by IOP Publishing Ltd.

King's Authors


Motivated by the phenomenon of coherent perfect absorption, we study the shape of the deepest dips in the frequency-dependent single-channel reflection of waves from a cavity with spatially uniform losses. We show that it is largely determined by non-orthogonality factors O nn of the eigenmodes associated with the non-selfadjoint effective Hamiltonian. For cavities supporting chaotic ray dynamics we then use random matrix theory to derive, fully non-perturbatively, the explicit distribution of the non-orthogonality factors for systems with both broken and preserved time reversal symmetry. The results imply that O nn are heavy-tail distributed. As a by-product, we derive an explicit non-perturbative expression for the resonance density in a single-channel chaotic systems in a much simpler form than available in the literature.

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