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

doi:10.1088/1751-8121/ac6717

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

Mathematics

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Article number	224013
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	55
Issue number	22
DOIs	https://doi.org/10.1088/1751-8121/ac6717
Publication status	Published - 7 Jun 2022

Keywords

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

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10.1088/1751-8121/ac6717

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

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. ",

keywords = "coherent perfect absorption, eigenvector nonorthogonality, non-Hermitian random matrices, resonances in chaotic quantum scattering",

author = "Fyodorov, {Yan V.} and Mohammed Osman",

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 {\textquoteleft}Random Hessians and Jacobians: theory and applications{\textquoteright}. Publisher Copyright: {\textcopyright} 2022 The Author(s). Published by IOP Publishing Ltd.",

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T1 - Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities

AU - Fyodorov, Yan V.

AU - Osman, Mohammed

N1 - 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.

PY - 2022/6/7

Y1 - 2022/6/7

N2 - 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.

AB - 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.

KW - coherent perfect absorption

KW - eigenvector nonorthogonality

KW - non-Hermitian random matrices

KW - resonances in chaotic quantum scattering

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U2 - 10.1088/1751-8121/ac6717

DO - 10.1088/1751-8121/ac6717

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AN - SCOPUS:85130713928

SN - 1751-8113

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

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M1 - 224013

ER -

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

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