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Physical Review C

Correlations between low-lying yrast states for s d bosons with random interactions

Yi Lu, Y. M. Zhao, N. Yoshida, A. Arima

Published Dec 19, 2014• 7 citations
Publisher

Abstract

In this paper we study low-lying states of $sd$ bosons under random interactions. We find that the yrast states are highly correlated, regardless of whether the ground state spin is zero or not. Many of the random samplings in the random ensemble well overlap with predictions of the U(5) limit in the interacting boson model.

DOI
10.1103/physrevc.90.064313

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In this paper we study low-lying states of sdsdsd bosons under random interactions. We find that the yrast states are highly correlated, regardless of whether the ground state spin is zero or not. Many of the random samplings in the random ensemble well overlap with predictions of the U(5) limit in the interacting boson model.
In this work we study the yrast states of sd\mathit{sd}sd-boson systems in the presence of random interactions. It is found that the yrast states with spin-zero ground states among the random ensemble exhibit strong correlations, characterized by anharmonic vibration, sss-boson or ddd-boson condensation, as well as vibrational and rotational motions. We study these correlations explicitly based on their wave functions and the features of two-body interactions in the random ensemble.
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.
We continue a series of numerical experiments on many-body systems with random two-body interactions, by examining correlations in ratios in excitation energies of yrast J=0,2,4,6,8J=0,2,4,6,8J=0,2,4,6,8 states. Previous studies, limited only to J=0,2,4J=0,2,4J=0,2,4 states, had shown strong correlations in boson systems but not fermion systems. By including $J\ensuremath{\geqslant}6$ states and considering different scatter plots, strong correlations between ratios of yrast excitation energies appear in both boson and fermion systems. Such correlations agree with real nuclear data and include the well-known limits of seniority, vibrations, and rotations.
Low-lying states in nuclei are investigated using an ensemble of random interactions. Both in the nuclear shell model and in the interacting boson model we find a dominance of JP=0+J^P=0^+JP=0+ ground states. It is shown that this feature is not due to time reversal symmetry. In the shell model, evidence is found for the occurrence of pairing properties, and in the interacting boson model for both vibrational and rotational band structures. Our results suggest that these features represent general and robust properties of the model space, and do not depend on details of the interactions.
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 problem of random interactions leading to regular spectra in shell model type simulations is described. The key results are reviewed alnog with a selection of the explanations. A model system of N particles on 2 spin levels having random 2-body collisions that conserve angular momentum is examined. Preliminary results are described, including the ground state spin distributions peaked at extreme values of angular momentum, signatures of rotational bands, and smooth parabolic yrast lines. A simple random matrix theory analysis shows signatures of quantum chaos in the level spacing distribution and the Δ3 statistic.