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 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 $\mathcal{P}(O_{nn})$ 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 $\mathcal{P}(O_{nn}\gg 1)\sim O_{nn}^{-3}$.

References in corpus (65)

• Coherent Perfect Absorbers: Time-reversed Lasers
• Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
• Coherent perfect absorbers: linear control of light with light
• Eigenvector statistics in non-Hermitian random matrix ensembles
• Truncations of random unitary matrices
• Random Matrices close to Hermitian or unitary: overview of methods and results
• Universal Impedance Fluctuations in Wave Chaotic Systems
• Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering
• Quantum limit of the laser linewidth in chaotic cavities and statistics of residues of scattering matrix poles
• Distribution of the quantum mechanical time-delay matrix for a chaotic cavity
• Distribution of reflection coefficients in absorbing chaotic microwave cavities
• Statistics of resonance width shifts as a signature of eigenfunction non-orthogonality
• Wigner time delay and related concepts -- Application to transport in coherent conductors
• Wigner time-delay distribution in chaotic cavities and freezing transition
• S-matrix poles for chaotic quantum systems as eigenvalues of complex symmetric random matrices: from isolated to overlapping resonances
• An exact formula for general spectral correlation function of random Hermitian matrices
• Quantum Versus Classical Decay Laws in Open Chaotic Systems
• Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption
• Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: Application to the time-delay problem
• Statistics of Resonances and Delay Times in Random Media: Beyond Random Matrix Theory
• Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles
• Resonance widths in open microwave cavities studied by harmonic inversion
• Parametric Correlations of Scattering Phase Shifts and Fluctuations of Delay Times in Few-Channel Chaotic Scattering
• Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach
• Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption
• Correlations of Eigenvectors for Non-Hermitian Random-Matrix Models
• Characterization of Fluctuations of Impedance and Scattering Matrices in Wave Chaotic Scattering
• Statistics of S-matrix poles in Few-Channel Chaotic Scattering: Crossover from Isolated to Overlapping Resonances
• Time Delay Correlations in Chaotic Scattering: Random Matrix Approach
• Spectral Theory of Sparse Non-Hermitian Random Matrices
• On the statistics of resonances and non-orthogonal eigenfunctions in a model for single-channel chaotic scattering
• Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers
• Perfect Absorption in Complex Scattering Systems with or without Hidden Symmetries
• Tau-Function Theory of Quantum Chaotic Transport with beta=1,2,4
• Parametric Correlations of Phase Shifts and Statistics of Time Delays in Quantum Chaotic Scattering: Crossover between Unitary and Orthogonal Symmetries
• The distribution of overlaps between eigenvectors of Ginibre matrices
• On statistics of bi-orthogonal eigenvectors in real and complex Ginibre ensembles: combining partial Schur decomposition with supersymmetry
• Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems
• Universal statistics of the local Green's function in quantum chaotic systems with absorption
• Experimental Width Shift Distribution: A Test of Nonorthogonality for Local and Global Perturbations
• Statistics of delay times in mesoscopic systems as a manifestation of eigenfunction fluctuations
• Distribution of zeros of the S-matrix of chaotic cavities with localized losses and Coherent Perfect Absorption: non-perturbative results
• Transmission zeros and ultrasensitive detection in complex systems
• Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem
• On-demand coherent perfect absorption in complex scattering systems: time delay divergence and enhanced sensitivity to perturbations
• Selectively exciting quasi-normal modes in open disordered systems
• Unveiling the significance of eigenvectors in diffusing non-hermitian matrices by identifying the underlying Burgers dynamics
• Generalization of Wigner Time Delay to Sub-Unitary Scattering Systems
• Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach
• Condition numbers for real eigenvalues in the real Elliptic Gaussian ensemble
• A Note on Mixed Matrix Moments for the Complex Ginibre Ensemble
• Statistical distribution of the Wigner-Smith time-delay matrix moments for chaotic cavities
• Wigner-Smith time-delay matrix in chaotic cavities with non-ideal contacts
• Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas
• From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behavior
• Full Dysonian dynamics of the complex Ginibre ensemble
• Universal eigenvector statistics in a quantum scattering ensemble
• Impact of non-Hemiticity on modal strength and correlation in transmission through random open cavities
• On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials
• Statistics of time delay and scattering correlation functions in chaotic systems I. Random Matrix Theory
• Chaotic Scattering with Localized Losses: S-Matrix Zeros and Reflection Time Difference for Systems with Broken Time Reversal Invariance
• Reflection Time Difference as a probe of S-matrix Zeroes in Chaotic Resonance Scattering
• Resonance Scattering of Waves in Chaotic Systems
• Universal eigenvector correlations in quaternionic Ginibre ensembles
• Distribution of the Wigner-Smith time-delay matrix for chaotic cavities with absorption and coupled Coulomb gases

Cited by in corpus (4)

• Reflectionless Programmable Signal Routers
• Extreme eigenvalues and the emerging outlier in rank-one non-Hermitian deformations of the Gaussian Unitary Ensemble
• Condition numbers for real eigenvalues of real elliptic ensemble: weak non-normality at the edge
• Eigenvalue and pseudospectrum processes generated by nonnormal Toeplitz matrices with rank 1 perturbations