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Motivated by the phenomenon of Coherent Perfect Absorption, we study theshape of the deepest minima in the frequency-dependent single-channelreflection of waves from a cavity with spatially uniform losses. We show thatit is largely determined by non-orthogonality factors $O_{nn}$ of theeigenmodes associated with the non-selfadjoint effective Hamiltonian. Forcavities supporting chaotic ray dynamics we then use random matrix theory toderive, fully non-perturbatively, the explicit probability density ${\calP}(O_{nn})$ of the non-orthogonality factors for systems with both broken andpreserved time reversal symmetry. The results imply that $O_{nn}$ areheavy-tail distributed, with the universal tail ${\cal P}(O_{nn}\gg 1)\simO_{nn}^{-3}$.

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