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arXiv:nucl-th/0508019 · Physical Review C

Robustness of regularities for energy centroids in the presence of random interactions

Y. M. Zhao, A. Arima, N. Yoshida, K. Ogawa, Naotaka Yoshinaga, V. K. B. Kota

Published Dec 20, 2005• 6 citations
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Abstract

In this paper we study energy centroids such as those with fixed spin and isospin and those with fixed irreducible representations for both bosons and fermions, in the presence of random two-body and/or three-body interactions. Our results show that regularities of energy centroids of fixed-spin states reported in earlier works are very robust in these more complicated cases. We suggest that these behaviors might be intrinsic features of quantum many-body systems interacting by random forces.

DOI
10.1103/physrevc.72.064314

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In this paper we study energy centroids such as those with fixed spin and isospin and those with fixed irreducible representations for both bosons and fermions, in the presence of random two-body and/or three-body interactions. Our results show that regularities of energy centroids of fixed-spin states reported in earlier works are very robust in these more complicated cases. We suggest that these behaviors might be intrinsic features of quantum many-body systems interacting by random forces.
In this paper we study the behavior of energy centroids (denoted as EI‾\overline{{E}_{I}}EI​​) of spin I states in the presence of random two-body interactions, for systems ranging from very simple systems (e.g., single-j shell for very small j) to very complicated systems (e.g., many-j shells with different parities and with isospin degree of freedom). Regularities of EI‾\overline{{E}_{I}}EI​​'s discussed in terms of the so-called geometric chaoticity (or quasi-randomness of two-body coefficients of fractional parentage) in earlier works are found to hold even for very simple systems in which one cannot assume geometric chaoticity. It is shown that the inclusion of isospin and parity does not ``break'' the regularities of EI‾\overline{{E}_{I}}EI​​'s.
Regular structures generated by random interactions in energy centroids defined over irreducible representations (irreps) of some of the group symmetries of the interacting boson models sdIBM, sdgIBM, sdIBM-T and sdIBM-ST are studied by deriving trace propagations equations for the centroids.It is found that, with random interactions, the lowest and highest group irreps in general carry most of the probability for the corresponding centroids to be lowest in energy.This generalizes the result known earlier, via numerical diagonalization, for the more complicated fixed spin (J) centroids where simple trace propagation is not possible.
Regular structures generated by random interactions in energy centroids defined over irreducible representations (irreps) of some of the group symmetries of the interacting boson models sdIBM, sdgIBM, sdIBM-T, and sdIBM-ST are studied by deriving trace propagation equations for the centroids. It is found that, with random interactions, the lowest and highest group irreps in general carry most of the probability for the corresponding centroids to be lowest in energy. This generalizes the result known earlier, via numerical diagonalization, for the more complicated fixed spin J centroids where simple trace propagation is not possible.