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

Yan V. Fyodorov*, Mohammed Osman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number224013
JournalJournal of Physics A: Mathematical and Theoretical
Volume55
Issue number22
DOIs
Publication statusPublished - 7 Jun 2022

Keywords

  • coherent perfect absorption
  • eigenvector nonorthogonality
  • non-Hermitian random matrices
  • resonances in chaotic quantum scattering

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