Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
arXiv:1001.2422 · doi:10.1103/RevModPhys.82.2845
Abstract
The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by a survey of phenomenological approaches to CN scattering. The implementation of a random-matrix approach into scattering theory leads to a statistical theory of CN reactions. Since RMT applies generically to chaotic quantum systems, that theory is, at the same time, a generic theory of quantum chaotic scattering. It uses a minimum of input parameters (average S-matrix and mean level spacing of the CN). Predictions of the theory are derived with the help of field-theoretical methods adapted from condensed-matter physics and compared with those of phenomenological approaches. Thorough tests of the theory are reviewed, as are applications in nuclear physics, with special attention given to violation of symmetries (isospin, parity) and time-reversal invariance.
50 pages, 26 figures
References in corpus (54)
- Random-Matrix Theory of Quantum Transport
- An Improved Experimental Limit on the Electric Dipole Moment of the Neutron
- Isospin Asymmetry in Nuclei and Neutron Stars
- The Statistical Theory of Quantum Dots
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Random Matrices and Chaos in Nuclear Physics
- Quantum mechanical time-delay matrix in chaotic scattering
- Periodic-Orbit Theory of Level Correlations
- Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
- Nuclear Parity-Violation in Effective Field Theory
- GENERALIZED CIRCULAR ENSEMBLE OF SCATTERING MATRICES FOR A CHAOTIC CAVITY WITH NON-IDEAL LEADS
- Random Matrices close to Hermitian or unitary: overview of methods and results
- Almost-Hermitian Random Matrices: Eigenvalue Density in the Complex Plane
- First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
- Continuum Shell Model
- Charge Symmetry Breaking and QCD
- Random Matrices and Chaos in Nuclear Spectra
- 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
- Quantum Chaotic Scattering in Microwave Resonators
- S-matrix poles for chaotic quantum systems as eigenvalues of complex symmetric random matrices: from isolated to overlapping resonances
- Proton-Neutron Coupling in the Gamow Shell Model: the Lithium Chain
- Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: Application to the time-delay problem
- Universality of Random-Matrix Results for non-Gaussian Ensembles
- Resonance widths in open microwave cavities studied by harmonic inversion
- Geometric chaoticity leads to ordered spectra for randomly interacting fermions
- 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
- Charge Symmetry at the Partonic Level
- A Simple Mode on a Highly Excited Background: Collective Strength and Damping in the Continuum
- Parametric Correlations of Phase Shifts and Statistics of Time Delays in Quantum Chaotic Scattering: Crossover between Unitary and Orthogonal Symmetries
- Crossover from Orthogonal to Unitary Symmetry for Ballistic Electron Transport in Chaotic Microstructures
- Induced Violation of Time-Reversal Invariance in the Regime of Weakly Overlapping Resonances
- Large Petermann factor in chaotic cavities with many scattering channels
- Coupled Microwave Billiards as a Model for Symmetry Breaking
- Statistics of delay times in mesoscopic systems as a manifestation of eigenfunction fluctuations
- Correlation functions of scattering matrix elements in microwave cavities with strong absorption
- Test of Parity-Conserving Time-Reversal Invariance Using Polarized Neutrons and Nuclear Spin Aligned Holmium
- Induced Time-Reversal Symmetry Breaking Observed in Microwave Billiards
- Open system of interacting fermions: Statistical properties of cross sections and fluctuations
- Superscars in billiards -- A model for doorway states in quantum spectra
- Statistical Theory of Parity Nonconservation in Compound Nuclei
- Chaotic Scattering in the Regime of Weakly Overlapping Resonances
- Ericson fluctuations in an open, deterministic quantum system: theory meets experiment
- Cross-Section Fluctuations in Chaotic Scattering
- Quantal Consequences of Perturbations Which Destroy Structurally Unstable Orbits in Chaotic Billiards
- Internal chaos in an open quantum system: From Ericson to conductance fluctuations
- R-matrix theory of driven electromagnetic cavities
- Scattering a pulse from a chaotic cavity: Transitioning from algebraic to exponential decay
- Abundance of Ground States with Positive Parity
- Testing T Invariance in the Interaction of Slow Neutrons with Aligned Nuclei
- Photonuclear Reactions induced by Intense Short Laser Pulses
- The Neutron EDM Experiment
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- Distribution of Partial Neutron Widths for Nuclei close to a Maximum of the Neutron Strength Function
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- Statistical analysis of excitation energies in the actinide and rare-earth nuclei
- Correlation functions and correlation widths in Quantum-Chaotic Scattering for mesoscopic systems and nuclei
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- Statistical-model description of decay from compound-nucleus resonances
- Derivation of K-matrix reaction theory in a discrete basis formalism
- Bivariate -normal distribution for transition strengths distribution from many-particle random matrix ensembles generated by -body interactions
- Wigner-Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity
- Missing level statistics in a dissipative microwave resonator with partially violated time-reversal invariance
- Multiple scattering model of the quantum random Lorentz gas
- Sparse random Hamiltonians are quantumly easy
- Current Status of Nuclear Physics Research
- Distribution of the Wigner-Smith time-delay matrix for chaotic cavities with absorption and coupled Coulomb gases
- A Model for Scattering with Proliferating Resonances: Many Coupled Square Wells
- Resonance distribution in the quantum random Lorentz gas
- Combinatorial problems in the semiclassical approach to quantum chaotic transport
- Exit-Channel Suppression in Statistical Reaction Theory
- One plus two-body random matrix ensembles with parity: Density of states and parity ratios
- Complexity and instability of quantum motion near a quantum phase transition
- Scattering Statistics in Nonlinear Wave Chaotic Systems
- de Broglie-Bohm analysis of a nonlinear membrane: From quantum to classical chaos
- Digital Quantum Simulation, Learning of the Floquet Hamiltonian, and Quantum Chaos of the Kicked Top
- Time-Reversal Symmetry Breaking and Decoherence in Chaotic Dirac Billiards
- Investigation of the enhancement factor in the regime of semi-Poisson statistics in a singular microwave cavity
- Global correlation matrix spectra of the surfacetemperature of the Oceans from Random MatrixTheory to Poisson fluctuations
- Deviations from the Porter-Thomas Distribution due to Nonstatistical Decay below the Nd Neutron Separation Threshold
- Statistics of a simple transmission mode on a lossy chaotic background
- Power-law intensity distribution in -decay cascades -- Nuclear Structure as a Scale-Free Random Network
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- Reply to the Comment of S. Ayik and D. Lacroix, posted as arXiv:1909.1361v1, on the recent article "Fission Dynamics of 240Pu from Saddle-to-Scission and Beyond" by Bulgac et al, published as Phys. Rev. C 100, 034615 (2019)
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