Two-Body Random Ensembles: From Nuclear Spectra to Random Polynomials

Abstract

The two-body random ensemble (TBRE) for a many-body bosonic theory is mapped to a problem of random polynomials on the unit interval. In this way one can understand the predominance of 0+ ground states, and analytic expressions can be derived for distributions of lowest eigenvalues, energy gaps, density of states and so forth. Recently studied nuclear spectroscopic properties are addressed.

8 pages, 4 figures. To appear in Physical Review Letters

References in corpus (5)

• Band structure from random interactions
• Generalized seniority from random Hamiltonians
• On the dominance of J(P)=0(+) ground states in even-even nuclei from random two-body interactions
• Robust Nuclear Observables and Constraints on Random Interactions
• Collective states in nuclei and many-body random interactions

Cited by in corpus (21)

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• Nuclear Structure, Random Interactions and Mesoscopic Physics
• 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
• Spectroscopy with random and displaced random ensembles
• Ground-State Magnetization for Interacting Fermions in a Disordered Potential : Kinetic Energy, Exchange Interaction and Off-Diagonal Fluctuations
• Mean-field analysis of interacting boson models with random interactions
• Odd-even binding effect from random two-body interactions
• A simple approach to the angular momentum distribution in the ground states of many-body systems
• Towards understanding the probability of $0^{+}$ ground states in even-even many-body systems
• Generic Rotation in a Collective SD Nucleon-Pair Subspace
• Regular spectra in the vibron model with random interactions
• Geometry of random interactions
• Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states
• Many-body Systems Interacting via a Two-body Random Ensemble: average energy of each angular momentum
• Comment on `Two-body random ensembles: from nuclear spectra to random polynomials
• Angular momentum I ground state probabilities of boson systems interacting by random interactions
• Ground State Properties of Many-Body Systems in the Two-Body Random Ensemble and Random Matrix Theory
• Ground-state energy distribution of disordered many-body quantum systems
• One plus two-body random matrix ensembles with parity: Density of states and parity ratios
• Ground state spin 0${}^{+}$ dominance of many-body systems with random interactions and related topics