Random Matrices and Chaos in Nuclear Physics

Abstract

The authors review the evidence for the applicability of random--matrix theory to nuclear spectra. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately: quantum chaos) in nuclei whenever random--matrix predictions are fulfilled. An introduction into the basic concepts of random--matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random--matrix ensembles patterned after the shell model such as the embedded two--body ensemble, the two--body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground--state regions of strongly deformed nuclei.

54 pages, 28 figures

References in corpus (13)

• Periodic-Orbit Theory of Level Correlations
• Random Matrices and Chaos in Nuclear Spectra
• Regularities of Many-body Systems Interacting by a Two-body Random Ensemble
• Distribution of spectral widths and preponderance of spin-0 ground states in nuclei
• Correlations in Nuclear Masses
• The Two-Body Random Ensemble in Nuclei
• Spin measurements for 147Sm+n resonances: Further evidence for non-statistical effects
• Origin of chaos in the spherical nuclear shell model: role of symmetries
• Patterns of the ground states in the presence of random interactions: nucleon systems
• Nuclear Masses, Chaos, and the Residual Interaction
• Level density of a Fermi gas: average growth and fluctuations
• Interaction of Regular and Chaotic States
• On the ground--state energy of finite Fermi systems

Cited by in corpus (152)

• Light fields in complex media: mesoscopic scattering meets wave control
• Radioactive decays at limits of nuclear stability
• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Magnetic dipole excitations in nuclei: elementary modes of nucleonic motion
• Quantum Chaos in Ultracold Collisions of Erbium
• Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
• Cleaning large correlation matrices: tools from random matrix theory
• Statistical Aspects of Ultracold Resonant Scattering
• Physics of the Riemann Hypothesis
• Emergence of chaotic scattering in ultracold Er and Dy
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
• Effects of symmetry breaking in finite quantum systems
• Production of Medical Radioisotopes with High Specific Activity in Photonuclear Reactions with $\gamma$ Beams of High Intensity and Large Brilliance
• Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model
• Quantum Chaotic Scattering in Microwave Resonators
• Reaction rates for the s-process neutron source 22Ne+α
• Power spectrum analysis and missing level statistics of microwave graphs with violated time reversal invariance
• Probing symmetries of quantum many-body systems through gap ratio statistics
• Chaos and ergodicity across the energy spectrum of interacting bosons
• Extreme Decoherence and Quantum Chaos
• Extreme statistics and spacing distribution in a Brownian gas correlated by resetting
• Anomalous fluctuations of s-wave reduced neutron widths of ${}^{192,194}$Pt resonances
• Random Matrix Ensemble for the Level Statistics of Many-Body Localization
• Electric and magnetic dipole modes in high-resolution inelastic proton scattering at $0^{\circ }$
• Higher order spacing ratios in random matrix theory and complex quantum systems
• Fine structure of the isovector giant dipole resonance in 208Pb: Characteristic scales and level densities
• Chaotic scattering of highly excited strings
• Expanding Nuclear Physics Horizons with the Gamma Factory
• Spectral statistics of molecular resonances in erbium isotopes: How chaotic are they?
• Resonances in open quantum maps
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Long-lived complexes and signatures of chaos in ultracold K2+Rb collisions
• Partial time-reversal invariance violation in a flat, superconducting microwave cavity with the shape of a chaotic Africa billiard
• Consolidating the concept of low-energy magnetic dipole decay radiation
• Chaos and regularity in the doubly magic nucleus 208Pb
• Spectral properties of Dirac billiards at the van Hove singularities
• Distribution of Partial Neutron Widths for Nuclei close to a Maximum of the Neutron Strength Function
• Objectivity (or lack there of): a comparison between predictions of quantum Darwinism and spectrum broadcast structure
• Nearest neighbor spacing distribution of prime numbers and quantum chaos
• Spreading widths of giant resonances in spherical nuclei: damped transient response
• Will a physicist prove the Riemann Hypothesis?
• Predominance of Prolate Nuclear Deformations Emerging from Many-Body Interactions
• Probability Distribution of the Ratio of Consecutive Level Spacings in Interacting Particle Systems
• Reduced neutron widths in the nuclear data ensemble: Experiment and theory do not agree
• Missing-level statistics in classically chaotic quantum systems with symplectic symmetry
• Nuclear Excitation by a Zeptosecond Multi--MeV Laser Pulse
• Exact distribution of spacing ratios for random and localized states in quantum chaotic systems
• Statistics of Chaotic Resonances in an Optical Microcavity
• Modification of the Porter-Thomas distribution by rank-one interaction
• Magnetic Field Control of the Quantum Chaotic Dynamics of Hydrogen Analogues in an Anisotropic Crystal Field
• Role of non-collective excitations in low-energy heavy-ion reactions
• Symmetry deduction from spectral fluctuations in complex quantum systems
• Equivalence of replica and cavity methods for computing spectra of sparse random matrices
• Wigner-Smith time-delay matrix in chaotic cavities with non-ideal contacts
• Coherent and stochastic contributions of compound resonances in atomic processes: Electron recombination, photoionization and scattering
• Integer moments of complex Wishart matrices and Hurwitz numbers
• Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption
• Chaos in the Bose-Hubbard model and random two-body Hamiltonians
• Experimental investigation of distributions of the off-diagonal elements of the scattering and the Wigner's $\hat{K}$ matrices for networks with broken time reversal invariance
• Many-body quantum dynamics of initially trapped systems due to a Stark potential --- thermalization vs. Bloch oscillations
• Porter-Thomas distribution in unstable many-body systems
• Isomeric cross sections of fast-neutron induced reactions on ${}^{197}$Au
• Avoided level crossing statistics in open chaotic billiards
• Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison
• First clear evidence of quantum chaos in the bound states of an atomic nucleus
• Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
• Laser-Nucleus Interactions: The Quasiadiabatic Regime
• Nuclear level densities and $\gamma$-ray strength functions in ${}^{120,124}$Sn isotopes: impact of Porter-Thomas fluctuations
• Quantum work for sudden quenches in Gaussian random Hamiltonians
• Spectral analysis of two-dimensional Bose-Hubbard models
• Temperature of a single chaotic eigenstate
• Theoretical descriptions of compound-nuclear reactions: open problems & challenges
• A novel Machine-Learning method for spin classification of neutron resonances
• Resonance width distribution for open quantum systems
• Pentahedral volume, chaos, and quantum gravity
• Random matrix analysis of deep neural network weight matrices
• A maximum likelihood method to correct for missed levels based on the ${\Delta }_3(L)$ statistic
• Neutron Resonance Data Exclude Random Matrix Theory
• The chaotic emergence of thermalization in highly excited string decays
• Interaction effects in a chaotic graphene quantum billiard
• Using the ${\Delta }_3$ statistic to test for missed levels in mixed sequence neutron resonance data
• Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics
• Reappraisal of the limit on the variation in $\alpha$ implied by Oklo
• Superposition and higher-order spacing ratios in random matrix theory with application to complex systems
• Work statistics for sudden quenches in interacting quantum many-body systems
• Level density of 2+ states in 40Ca from high energy-resolution (p,p') experiments
• Quantum Chaos in the Heisenberg Spin Chain: the Effect of Dzyaloshinskii-Moriya Interaction
• Dynamical typicality of embedded quantum systems
• Random matrix ensemble with random two-body interactions in presence of a mean-field for spin one boson systems
• Level density of the $sd$-nuclei $-$ statistical shell-model predictions
• Chaotic scattering in the presence of a dense set of overlapping Feshbach resonances
• Projected shell model description of nuclear level density: Collective, pair-breaking, and multiquasiparticle regimes in even-even nuclei
• Effect of proximity-induced spin-orbit coupling in graphene mesoscopic billiards
• Time scales in nuclear giant resonances
• Spectral statistics of rare-earth nuclei: Investigation of shell model configuration effect
• Quantum chaos in Feshbach resonances of the ErYb system
• Sensitivity of the spectral form factor to short-range level statistics
• Integrability in time-dependent systems with one degree of freedom
• The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes
• Mahaux-Weidenmüller approach to cavity quantum electrodynamics and complete resonant down-conversion of the single photon frequency
• Cross-Section Fluctuations in Chaotic Scattering Systems
• Porter-Thomas fluctuations in complex quantum systems
• A simple approach to the chaos-order contributions in nuclear spectra
• Fractal Universality in Near-Threshold Magnetic Lanthanide Dimers
• Statistical analysis of excitation energies in the actinide and rare-earth nuclei
• Random matrix analysis of the monopole strength distribution in ${}^{208}$Pb
• Exact numerical methods for a many-body Wannier Stark system
• Reaction rates for the ${}^{39}$K(p,$\gamma$)${}^{40}$Ca reaction
• Photonuclear Reactions induced by Intense Short Laser Pulses
• Distribution of the Wigner-Smith time-delay matrix for chaotic cavities with absorption and coupled Coulomb gases
• One plus two-body random matrix ensembles with parity: Density of states and parity ratios
• Proposed search for T-odd, P-even interactions in spectra of chaotic atoms
• Robust correlations between quadrupole moments of low-lying $2^{+}$ states within random-interaction ensembles
• Approximate treatment of noncommutative curvature in quartic matrix model
• A Model for Scattering with Proliferating Resonances: Many Coupled Square Wells
• Lowest eigenvalue of the nuclear shell model Hamiltonian
• Random Matrix Ensembles in Hyperchaotic Classical Dissipative Dynamical Systems
• Laser-nucleus interactions in the sudden regime
• Power-law intensity distribution in $\gamma$-decay cascades -- Nuclear Structure as a Scale-Free Random Network
• Deviations from the Porter-Thomas Distribution due to Nonstatistical $\gamma$ Decay below the ${}^{150}$Nd Neutron Separation Threshold
• Coupled unidirectional chaotic microwave graphs
• Investigation of the enhancement factor in the regime of semi-Poisson statistics in a singular microwave cavity
• Statistical Nuclear Spectroscopy with $q$-normal and bivariate $q$-normal distributions and $q$-Hermite polynomials
• Non-equilibrium Green's function approach to low-energy fission dynamics: fluctuations in fission reactions
• New equilibrium ensembles for isolated quantum systems
• Time-reversal Invariance Violation and Quantum Chaos Induced by Magnetization in Ferrite-Loaded Resonators
• Open Problems in Applying Random-Matrix Theory to Nuclear Reactions
• Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics
• Ordered Level Spacing Distribution in Embedded Random Matrix Ensembles
• Classes of non-Gaussian random matrices: long-range eigenvalue correlations and non-ergodic extended eigenvectors
• Numerical Simulation of GUE Two-Point Correlation and Cluster Functions
• Application of the shift-invert Lanczos algorithm to a non-equilibrium Green function for transport problems
• A transition in the spectral statistics of quantum optical model by different electromagnetic fields
• Experimental study of the distributions of off-diagonal scattering-matrix elements of quantum graphs with symplectic symmetry
• Appearance of Random Matrix Theory in Deep Learning
• The 2025 Evaluation of Experimental Thermonuclear Reaction Rates (ETR25)
• From Confinement to Chaos in AdS/CFT Correspondence via Non-equilibrium Local States
• Doorway States in the Random-Phase Approximation
• Robust upper limit on the neutron single-particle energy of the $i_{13/2}$ orbit
• Classical periodic trajectories and quantum scars in many-spin systems
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos
• A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics
• Manifestations of Isospin in Nearest Neighbor Spacing Distributions for the f-p Model Space
• Interaction patterns in diabetes mellitus II network: An RMT relation
• Test of the Porter-Thomas distribution with the total cross section autocorrelation function
• Solvable random matrix ensemble with a logarithmic weakly confining potential
• Transition-state dynamics in complex quantum systems
• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature
• Universal Relation between Spectral and Wavefunction Properties at Criticality
• Universality Emerging in a Universality: Derivation of the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation
• Universal Frequency Correlations and Recurrence Statistics of Complex Impedance Matrices
• Crystalline Spectral Form Factors