Nuclear Structure, Random Interactions and Mesoscopic Physics

Abstract

Standard concepts of nuclear physics explaining the systematics of ground state spins in nuclei by the presence of specific coherent terms in the nucleon-nucleon interaction were put in doubt by the observation that these systematics can be reproduced with high probability by randomly chosen rotationally invariant interactions. We review the recent development in this area, along with new original results of the authors. The self-organizing role of geometry in a finite mesoscopic system explains the main observed features in terms of the created mean field and correlations that are considered in analogy to the random phase approximation.

review paper; 54 pages with 16 figures

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Cited by in corpus (32)

• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Random Matrices and Chaos in Nuclear Physics
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
• Random Matrices and Chaos in Nuclear Spectra
• Regularities of Many-body Systems Interacting by a Two-body Random Ensemble
• Thermodynamic analogy for quantum phase transitions at zero temperature
• Distribution of spectral widths and preponderance of spin-0 ground states in nuclei
• Predominance of Prolate Nuclear Deformations Emerging from Many-Body Interactions
• The Two-Body Random Ensemble in Nuclei
• A new puzzle for random interaction
• Porter-Thomas distribution in unstable many-body systems
• Emergence of symmetry from random n-body interactions
• Lowest Eigenvalues of Random Hamiltonians
• High-lying single-particle modes, chaos, correlational entropy, and doubling phase transition
• Quantum phase transitions and collective enhancement of level density in odd-A and odd-odd nuclei
• Elastic enhancement factor as a quantum chaos probe
• Shell-model test of the rotational-model relation between static quadrupole moments Q(2^+_1), B(E2)'s, and orbital M1 transitions
• Abundance of Ground States with Positive Parity
• Regularities with random interactions in energy centroids defined by group symmetries
• Energy Centroids in the presence of random interactions
• Robust correlations between quadrupole moments of low-lying $2^{+}$ states within random-interaction ensembles
• Quadrupole collectivity in random two-body ensembles
• Open quantum systems and Random Matrix Theory
• One plus two-body random matrix ensembles with parity: Density of states and parity ratios
• Moments Method for Shell-Model Level Density
• Eigenvalues correlations and the distribution of ground state angular momenta for random many-body quantum systems
• Sensitivity analysis of random two-body interactions
• Channel cross-correlations in transport through complex media
• Global correlations between electromagnetic and spectroscopic properties of collective $2_1^{+}$ and $2_2^{+}$ states
• Robust upper limit on the neutron single-particle energy of the $i_{13/2}$ orbit
• Order, Collectivity, Structured Yrast Lines, and Correlated Energies in Random Bosonic Systems
• Replica Symmetry Breaking in Random Non-Hermitian Systems