Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review C

Collectivity of low-lying states under random two-body interactions

Y. M. Zhao, J. L. Ping, A. Arima

Published Nov 26, 2007• 10 citations
Publisher

Abstract

In this article we study the behavior of collectivity under random two-body interactions in the framework of the fermion dynamical symmetry model (FDSM). We found that a Hamiltonian with the SO(8) symmetry of the FDSM does not give vibrational and rotational modes under random interactions while a Hamiltonian with the SP(6) symmetry does. It is suggested that collective motions such as vibration and rotation are closely related not only to the quadruple-quadruple correlation in the Hamiltonian but also to the dynamical symmetries of the Hamiltonian.

DOI
10.1103/physrevc.76.054318

Related papers

Excited states of many-body systems in the fermion dynamical symmetry model with random interactions

G. J. Fu, Y. M. Zhao, J. L. Ping +1 more

In this Brief Report we investigate excited yrast states under random interactions in the framework of the fermion dynamical symmetry model, for the ensemble with spin-0 ground states. Interesting correlations are seen between ${R}_{6}$ and ${R}_{4}$ (where ${R}_{I}\ensuremath{\equiv}{E}_{{I}_{1}^{+}}/{E}_{{2}_{1}^{+}}$) by using the Mallmann plot, for cases with both SP(6) symmetry and SO(8) symmetry.

Physical Review C•Sep 23, 2013•9 citations

Collective behavior in random interaction

Calvin W. Johnson, Hai Ah Nam

Recent investigations have looked at the many-body spectra of random two-body interactions. In fermion systems, such as the interacting shell model, one finds pairing-like spectra, while in boson systems, such as IBM-1, one finds rotational and vibrational spectra. We discuss the search for random ensembles of fermion interactions that yield rotational and vibrational spectra, and in particular present results from a new ensemble, the ``random quadrupole-quadrupole ensemble''

arXiv:nucl-th/0601093•Revista Mexicana de Física•Jan 30, 2006•1 citation

Collective states in nuclei and many-body random interactions

R. Bijker, Alejandro Frank

Low-lying collective states in nuclei are investigated in the framework of the interacting boson model using an ensemble of random many-body interactions. It is shown that whenever the number of bosons is sufficiently large compared to the rank of the interactions, the spectral properties are characterized by a dominance of ${L}^{P}{=0}^{+}$ ground states and the occurrence of both vibrational and rotational band structures. This indicates that these features represent a general and robust property of the collective model space.

arXiv:nucl-th/0004002•Physical Review C•Jun 1, 2000•50 citations

Generic rotation in a collective SD nucleon-pair subspace

Y. M. Zhao, Stuart Pittel, R. Bijker +2 more

The low-lying collective states involving many nucleons interacting by the two-body random ensemble (TBRE) interactions are investigated in a collective $\mathrm{SD}$-pair subspace, with the collective pairs defined by the two-nucleon system. It is found that in this truncated pair subspace, collective vibrations arise naturally for a general TBRE Hamiltonian whereas collective rotations do not. A Hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the Hamiltonian is key to producing generic collective rotation.

arXiv:nucl-th/0206042•Physical Review C•Oct 17, 2002•28 citations

Random phase approximation studies in the fermion dynamical symmetry model: SO(8)

G. Wenes, Joseph N. Ginocchio

The SO(8) dynamical symmetry limit of the Fermion dynamical symmetry model is used to study various aspects of the quasiparticle random phase approximation. The zero frequency modes of the general quasiparticle random phase approximation are given in analytical form. The quasiparticle random phase approximation excitation energy and transition probability are derived in analytical form in the spherical limit of the general SO(8) Hamiltonian.

Physical Review C•Jun 1, 1989•1 citation

Quadrupole collectivity in the two-body random ensemble

Volha Abramkina, Alexander Volya

We conduct a systematic investigation of the nuclear collective dynamics that emerges in systems with two-body random interactions. We explore the development of the mean field and study its geometry. We investigate multipole collectivities in the many-body spectra and their dependence on the underlying two-body interaction Hamiltonian. The quadrupole-quadrupole interaction component appears to be dynamically dominating in the two-body random ensemble. This quadrupole coherence leads to rotational spectral features and thus suggests the formation of the deformed mean-field of a specific geometry.

arXiv:1105.1669•Physical Review C•Aug 25, 2011•6 citations
In this article we study the behavior of collectivity under random two-body interactions in the framework of the fermion dynamical symmetry model (FDSM). We found that a Hamiltonian with the SO(8) symmetry of the FDSM does not give vibrational and rotational modes under random interactions while a Hamiltonian with the SP(6) symmetry does. It is suggested that collective motions such as vibration and rotation are closely related not only to the quadruple-quadruple correlation in the Hamiltonian but also to the dynamical symmetries of the Hamiltonian.
In this Brief Report we investigate excited yrast states under random interactions in the framework of the fermion dynamical symmetry model, for the ensemble with spin-0 ground states. Interesting correlations are seen between R6{R}_{6}R6​ and R4{R}_{4}R4​ (where ${R}_{I}\ensuremath{\equiv}{E}_{{I}_{1}^{+}}/{E}_{{2}_{1}^{+}}$) by using the Mallmann plot, for cases with both SP(6) symmetry and SO(8) symmetry.
Low-lying collective states in nuclei are investigated in the framework of the interacting boson model using an ensemble of random many-body interactions. It is shown that whenever the number of bosons is sufficiently large compared to the rank of the interactions, the spectral properties are characterized by a dominance of LP=0+{L}^{P}{=0}^{+}LP=0+ ground states and the occurrence of both vibrational and rotational band structures. This indicates that these features represent a general and robust property of the collective model space.
The low-lying collective states involving many nucleons interacting by the two-body random ensemble (TBRE) interactions are investigated in a collective SD\mathrm{SD}SD-pair subspace, with the collective pairs defined by the two-nucleon system. It is found that in this truncated pair subspace, collective vibrations arise naturally for a general TBRE Hamiltonian whereas collective rotations do not. A Hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the Hamiltonian is key to producing generic collective rotation.
We conduct a systematic investigation of the nuclear collective dynamics that emerges in systems with two-body random interactions. We explore the development of the mean field and study its geometry. We investigate multipole collectivities in the many-body spectra and their dependence on the underlying two-body interaction Hamiltonian. The quadrupole-quadrupole interaction component appears to be dynamically dominating in the two-body random ensemble. This quadrupole coherence leads to rotational spectral features and thus suggests the formation of the deformed mean-field of a specific geometry.