arXiv:nucl-th/0503031 · Physical Review C

Regularities with random interactions in energy centroids defined by group symmetries

V. K. B. Kota

Published Apr 29, 2005• 8 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevc.71.041304

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Regularities with random interactions in energy centroids defined by group symmetries

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arXiv:nucl-th/0503031 · Physical Review C

Regularities with random interactions in energy centroids defined by group symmetries

V. K. B. Kota

Published Apr 29, 2005• 8 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevc.71.041304

Related papers

Regularities with random interactions in energy centroids defined by group symmetries

V. K. B. Kota

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 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.

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Random interactions in nuclei and extension of $0^+$ dominance in ground states to irreps of group symmetriesRandom interactions in nuclei and extension of $0^+$ dominance in ground states to irreps of group symmetries

V. K. B. Kota

Random one plus two-body hamiltonians invariant with respect to $O({\cal N}_1) \oplus O({\cal N}_2)$ symmetry in the group-subgroup chains $U({\cal N}) \supset U({\cal N}_1) \oplus U({\cal N}_2) \supset O({\cal N}_1) \oplus O({\cal N}_2)$ and $U({\cal N}) \supset O({\cal N}) \supset O({\cal N}_1) \oplus O({\cal N}_2)$ chains of a variety of interacting boson models are used to investigate the probability of occurrence of a given $(ω_1 ω_2)$ irreducible representation (irrep) to be the ground state in even-even nuclei; $[ω_1]$ and $[ω_2]$ are symmetric irreps of $O({\cal N}_1)$ and $O({\cal N}_2)$ respectively. Numerical results obtained for ${\cal N}_1 \geq 3, {\cal N}_2=1$ and ${\cal N}_1, {\cal N}_2 \geq 3$ situations are well explained by an extended Hartree-Bose mean-field analysis.Random one plus two-body hamiltonians invariant with respect to $O({\cal N}_1) \oplus O({\cal N}_2)$ symmetry in the group-subgroup chains $U({\cal N}) \supset U({\cal N}_1) \oplus U({\cal N}_2) \supset O({\cal N}_1) \oplus O({\cal N}_2)$ and $U({\cal N}) \supset O({\cal N}) \supset O({\cal N}_1) \oplus O({\cal N}_2)$ chains of a variety of interacting boson models are used to investigate the probability of occurrence of a given $(ω_1 ω_2)$ irreducible representation (irrep) to be the ground state in even-even nuclei; $[ω_1]$ and $[ω_2]$ are symmetric irreps of $O({\cal N}_1)$ and $O({\cal N}_2)$ respectively. Numerical results obtained for ${\cal N}_1 \geq 3, {\cal N}_2=1$ and ${\cal N}_1, {\cal N}_2 \geq 3$ situations are well explained by an extended Hartree-Bose mean-field analysis.

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Energy centroids of spin I states by random two-body interactions

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In this paper we study the behavior of energy centroids (denoted as $\overline{{E}_{I}}$ ) 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 $\overline{{E}_{I}}$ '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 $\overline{{E}_{I}}$ 's.In this paper we study the behavior of energy centroids (denoted as $\overline{{E}_{I}}$) 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 $\overline{{E}_{I}}$'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 $\overline{{E}_{I}}$'s.

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Random interactions in nuclei and extension of

0^+

dominance in ground states to irreps of group symmetries

Random one plus two-body hamiltonians invariant with respect to

O({\cal N}_1) \oplus O({\cal N}_2)

symmetry in the group-subgroup chains

U({\cal N}) \supset U({\cal N}_1) \oplus U({\cal N}_2) \supset O({\cal N}_1) \oplus O({\cal N}_2)

and

U({\cal N}) \supset O({\cal N}) \supset O({\cal N}_1) \oplus O({\cal N}_2)

chains of a variety of interacting boson models are used to investigate the probability of occurrence of a given

(ω_1 ω_2)

irreducible representation (irrep) to be the ground state in even-even nuclei;

[ω_1]

and

[ω_2]

are symmetric irreps of

O({\cal N}_1)

and

O({\cal N}_2)

respectively. Numerical results obtained for

{\cal N}_1 \geq 3, {\cal N}_2=1

and

{\cal N}_1, {\cal N}_2 \geq 3

situations are well explained by an extended Hartree-Bose mean-field analysis.

In this paper we study the behavior of energy centroids (denoted as

\overline{{E}_{I}}

) 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

\overline{{E}_{I}}

'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

\overline{{E}_{I}}

's.