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

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.

Automated summary

Motivated by coherent perfect absorption, this study investigates the shape of the deepest dips in the frequency-dependent single-channel reflection of waves from a cavity with spatially uniform losses. Non-orthogonality factors O(nn) of eigenmodes associated with the non-selfadjoint effective Hamiltonian play a major role in determining the shape. For cavities supporting chaotic ray dynamics, random matrix theory is used to derive the explicit distribution of non-orthogonality factors, revealing that they follow a heavy-tail distribution. Additionally, an explicit non-perturbative expression for the resonance density in single-channel chaotic systems is derived.