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

TL;DR

This paper investigates how non-orthogonality factors of eigenmodes influence the shape of reflection minima in lossy chaotic cavities, using random matrix theory to derive their probability distribution and universal tail behavior.

Contribution

It introduces a non-perturbative analysis of eigenfunction non-orthogonality in chaotic cavities and derives the universal distribution of non-orthogonality factors.

Findings

Non-orthogonality factors significantly shape reflection dips.

Derived explicit probability density for non-orthogonality factors.

Identified heavy-tail distribution with universal decay O_{nn}^{-3}.

Abstract

Motivated by the phenomenon of Coherent Perfect Absorption, we study the shape of the deepest minima 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 probability density ${\cal P}(O_{nn})$ 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, with the universal tail ${\cal P}(O_{nn}\gg 1)\sim O_{nn}^{-3}$.