arXiv:nucl-th/0612018 · Physical Review C

New puzzle for many-body systems with random two-body interactions

Calvin W. Johnson, Hai Ah Nam

Published Apr 25, 2007• 26 citations

Abstract

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 $J=0,2,4,6,8$ states. Previous studies, limited only to $J=0,2,4$ 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.

DOI: 10.1103/physrevc.75.047305

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arXiv:nucl-th/0612018 · Physical Review C

New puzzle for many-body systems with random two-body interactions

Calvin W. Johnson, Hai Ah Nam

Published Apr 25, 2007• 26 citations

arXiv HTML PDF

Abstract

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=0,2,4,6,8

states. Previous studies, limited only to

J=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.

DOI: 10.1103/physrevc.75.047305

Related papers

Order, collectivity, structured yrast lines, and correlated energies in random bosonic systems

D. Mulhall

Signatures of order and collectivity appear in a broad range of one and two level boson systems. Toy systems of $N$ particles on a single $j=3,\,4\dots 7$ level, and on 2 levels $(j_1,\,j_2)$ with $j_1+j_2 \leq 6$ were studied. Surprising novel features in the yrast lines were consistent with boson condensates. Strong signatures of order and collectivity were the norm. These included the usual energy ratios and quadrupole transition strengths for vibrational and rotational bands. There were pronounced correlations in energy ratios, sharp peaks in the Alga ratios and fractional collectivity across all the 1-level systems, as well as signatures of triaxialitySignatures of order and collectivity appear in a broad range of one and two level boson systems. Toy systems of $N$ particles on a single $j=3,\,4\dots 7$ level, and on 2 levels $(j_1,\,j_2)$ with $j_1+j_2 \leq 6$ were studied. Surprising novel features in the yrast lines were consistent with boson condensates. Strong signatures of order and collectivity were the norm. These included the usual energy ratios and quadrupole transition strengths for vibrational and rotational bands. There were pronounced correlations in energy ratios, sharp peaks in the Alga ratios and fractional collectivity across all the 1-level systems, as well as signatures of triaxiality

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A variable combination of realistic and random two-body interactions allows the study of collective properties [such as the energy spectra and $B(E2)$ transition strengths] in ${}^{44}\mathrm{Ti},$ ${}^{48}\mathrm{Cr},$ and ${}^{24}\mathrm{Mg}.$ It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the $B(E2)$ values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.A variable combination of realistic and random two-body interactions allows the study of collective properties [such as the energy spectra and $B(E2)$ transition strengths] in ${}^{44}\mathrm{Ti},$ ${}^{48}\mathrm{Cr},$ and ${}^{24}\mathrm{Mg}.$ It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the $B(E2)$ values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.

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We investigate the robustness of ``noncollective'' rotational behavior for nuclei with random two-body interactions in the framework of nuclear shell model. The normal $I(I+1)$ behavior of average excitation energy of yrast states is universal for both even-nucleon and odd-nucleon systems by two-body random ensemble. In some special random samplings, especially the samplings with spin- ${I}_{\mathrm{max}}$ ground state, the inverse noncollective rotational behavior is found for both even-nucleon and odd-nucleon systems in this paper. Interestingly, above rotational behaviors are still robust in the presence of random two-body interactions plus realistic single-particle energies.We investigate the robustness of ``noncollective'' rotational behavior for nuclei with random two-body interactions in the framework of nuclear shell model. The normal $I(I+1)$ behavior of average excitation energy of yrast states is universal for both even-nucleon and odd-nucleon systems by two-body random ensemble. In some special random samplings, especially the samplings with spin-${I}_{\mathrm{max}}$ ground state, the inverse noncollective rotational behavior is found for both even-nucleon and odd-nucleon systems in this paper. Interestingly, above rotational behaviors are still robust in the presence of random two-body interactions plus realistic single-particle energies.

Physical Review CNov 29, 20211 citation

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=0,2,4,6,8

states. Previous studies, limited only to

J=0,2,4

states, had shown strong correlations in boson systems but not fermion systems. By including

J\ensuremath{\geqslant}6

Signatures of order and collectivity appear in a broad range of one and two level boson systems. Toy systems of

N

particles on a single

j=3,\,4\dots 7

level, and on 2 levels

(j_1,\,j_2)

with

j_1+j_2 \leq 6

were studied. Surprising novel features in the yrast lines were consistent with boson condensates. Strong signatures of order and collectivity were the norm. These included the usual energy ratios and quadrupole transition strengths for vibrational and rotational bands. There were pronounced correlations in energy ratios, sharp peaks in the Alga ratios and fractional collectivity across all the 1-level systems, as well as signatures of triaxiality

In this work we study the yrast states of

\mathit{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,

s

-boson or

d

-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.

{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.

A variable combination of realistic and random two-body interactions allows the study of collective properties [such as the energy spectra and

B(E2)

transition strengths] in

{}^{44}\mathrm{Ti},

{}^{48}\mathrm{Cr},

and

{}^{24}\mathrm{Mg}.

It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the

B(E2)

values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.

We investigate the robustness of ``noncollective'' rotational behavior for nuclei with random two-body interactions in the framework of nuclear shell model. The normal

I(I+1)

behavior of average excitation energy of yrast states is universal for both even-nucleon and odd-nucleon systems by two-body random ensemble. In some special random samplings, especially the samplings with spin-

{I}_{\mathrm{max}}

ground state, the inverse noncollective rotational behavior is found for both even-nucleon and odd-nucleon systems in this paper. Interestingly, above rotational behaviors are still robust in the presence of random two-body interactions plus realistic single-particle energies.