Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering

Abstract

We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all n-point correlation functions in the complex plane. As a by-product, we establish the Ginibre-like statistics of resonances for many open channels. Our method is a combination of Itzykson-Zuber integration and a variant of nonlinear $\sigma -$model and can be applied when the use of orthogonal polynomials is problematic.

4 pages, no figures. Misprints corrected, some details on single-channel and many-channel cases are added

References in corpus (4)

• Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
• Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
• S-matrix poles for chaotic quantum systems as eigenvalues of complex symmetric random matrices: from isolated to overlapping resonances
• Statistics of S-matrix poles for chaotic systems with broken time reversal invariance: a conjecture

Cited by in corpus (70)

• Non-Hermitian Physics
• Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
• Truncations of random unitary matrices
• Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
• Random Matrices close to Hermitian or unitary: overview of methods and results
• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
• Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices
• Level statistics across the many--body localization transition
• Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation
• An exact formula for general spectral correlation function of random Hermitian matrices
• Statistics of Resonances and Delay Times in Random Media: Beyond Random Matrix Theory
• Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: Application to the time-delay problem
• From bound states to the continuum
• Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach
• On the statistics of resonances and non-orthogonal eigenfunctions in a model for single-channel chaotic scattering
• Random matrices beyond the Cartan classification
• Wishart and Anti-Wishart random matrices
• Toward understanding the microscopic origin of nuclear clustering
• Universal microscopic correlation functions for products of truncated unitary matrices
• Resonances in open quantum maps
• Generalizations of some integrals over the unitary group
• From closed to open 1D Anderson model: Transport versus spectral statistics
• Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kaehler manifolds
• Invariant $\beta$-Wishart ensembles, crossover densities and asymptotic corrections to the Marchenko-Pastur law
• Time Delay Correlations and Resonances in 1D Disordered Systems
• Distribution of zeros of the S-matrix of chaotic cavities with localized losses and Coherent Perfect Absorption: non-perturbative results
• On absolute moments of characteristic polynomials of a certain class of complex random matrices
• Moments of Wishart-Laguerre and Jacobi ensembles of random matrices: application to the quantum transport problem in chaotic cavities
• Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD
• The solution of a chiral random matrix model with complex eigenvalues
• Microscopic correlation functions for the QCD Dirac operator with chemical potential
• On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble
• Generalization of Wigner Time Delay to Sub-Unitary Scattering Systems
• Resonance width distribution for high-dimensional random media
• Cross-Section Fluctuations in Chaotic Scattering
• Statistics of eigenfunctions in open chaotic systems: a perturbative approach
• Critical statistics for non-Hermitian matrices
• The Statistics of Chaotic Tunnelling
• Statistics of Complex Wigner Time Delays as a counter of S-matrix poles: Theory and Experiment
• On matrix model partition functions for QCD with chemical potential
• Complex-valued information entropy measure for networks with directed links (digraphs). Application to citations by community agents with opposite opinions
• Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas
• Universal eigenvector statistics in a quantum scattering ensemble
• On the Anti-Wishart distribution
• On characteristic polynomials for a generalized chiral random matrix ensemble with a source
• Spectral Properties of the Jacobi Ensembles via the Coulomb Gas approach
• Chaotic Scattering with Localized Losses: S-Matrix Zeros and Reflection Time Difference for Systems with Broken Time Reversal Invariance
• Mode statistics in random lasers
• Reflection Time Difference as a probe of S-matrix Zeroes in Chaotic Resonance Scattering
• Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities
• Weakly bound systems, continuum effects, and reactions
• On the Correlation Functions of the Characteristic Polynomials of Non-Hermitian Random Matrices with Independent Entries
• Correlation Widths in Quantum--Chaotic Scattering
• Statistical Properties of Fano Resonances in Atomic and Molecular Photoabsorption
• Co-rank 1 projections and the randomised Horn problem
• Parametric spectral correlations in disordered and chaotic structures
• Low rank perturbations of large elliptic random matrices
• Extreme eigenvalues and the emerging outlier in rank-one non-Hermitian deformations of the Gaussian Unitary Ensemble
• Dynamics of a rank-one perturbation of a Hermitian matrix
• Open quantum systems and Random Matrix Theory
• Spectra of nearly Hermitian random matrices
• On the Spectrum of Random Anti-symmetric and Tournament Matrices
• Truncations of random symplectic unitary matrices
• Edge behavior of two-dimensional Coulomb gases near a hard wall
• Stochastic and Quantum Dynamics of Repulsive Particles: from Random Matrix Theory to Trapped Fermions
• Dynamics of a rank-one multiplicative perturbation of a unitary matrix
• Multiplicative non-Hermitian perturbations of classical $\beta$-ensembles
• Entanglement transitions induced by large deviations
• Entropy and singular-value moments of products of truncated random unitary matrices