A simple approach to the angular momentum distribution in the ground states of many-body systems

Abstract

We propose a simple approach to predict the angular momentum I ground state (I g.s.) probabilities of many-body systems that does not require the diagonalization of hamiltonians with random interactions. This method is found to be applicable to {\bf all} cases that have been discussed: even and odd fermion systems (both in single-j and many-j shells), and boson (both sd and sdg) systems. A simple relation for the highest angular momentum g.s. probability is found. Furthermore, it is suggested for the first time that the 0g.s. dominance in boson systems and in even-fermion systems is given by two-body interactions with specific features.

8 pages, 3 figures, to be published

References in corpus (6)

• Spectroscopy with random and displaced random ensembles
• Mean-field analysis of interacting boson models with random interactions
• Towards understanding the probability of $0^{+}$ ground states in even-even many-body systems
• Regular spectra in the vibron model with random interactions
• Nature of order from random two-body interactions
• Comment on `Two-body random ensembles: from nuclear spectra to random polynomials

Cited by in corpus (19)

• The Shell Model as Unified View of Nuclear Structure
• Random Matrices and Chaos in Nuclear Physics
• Random Matrices and Chaos in Nuclear Spectra
• 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
• Generic Rotation in a Collective SD Nucleon-Pair Subspace
• General pairing interactions and pair truncation approximations for fermions in a single-j shell
• Geometry of random interactions
• Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states
• Patterns of the ground states in the presence of random interactions: nucleon systems
• Many-body Systems Interacting via a Two-body Random Ensemble: average energy of each angular momentum
• Emergence of symmetry from random n-body interactions
• Angular momentum I ground state probabilities of boson systems interacting by random interactions
• A study of randomness, correlations and collectivity in the nuclear shell model
• Regularities with random interactions in energy centroids defined by group symmetries
• Energy Centroids of Spin $I$ States by Random Two-body Interactions
• Eigenvalues correlations and the distribution of ground state angular momenta for random many-body quantum systems
• Order, Collectivity, Structured Yrast Lines, and Correlated Energies in Random Bosonic Systems