Angular momentum distribution of the ground states in the presence of random interactions: Boson systems

Zhao, Y. M.; Yoshinaga, N.

doi:10.1103/physrevc.68.014322

Cited by 9 publications

(8 citation statements)

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“…For recent studies of random Hamiltonians for sd bosons, see Refs. [6][7][8][9][10][11][12].In Ref.[7], Bijker and Frank pointed out that the vibration and rotation are two important motions in sd-boson systems, even if random interactions are assumed. These two motions are characterized by the ratio of the first 4 + state energy with respect to the first 2 + state energy, that is, R 4 = E 4 + 1 /E 2 + 1 (in this paper, we define R I = E I + 1 /E 2 + 1 ).…”

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confidence: 99%

Correlations of excited states forsdbosons in the presence of random interactions

Lei¹,

Zhao²,

Yoshida³

2011

Phys. Rev. C

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In this work we study the yrast states of 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.Challenges of modern science reflect the twin themes of complexity and simplicity in many-body systems, and the structure of atomic nuclei provides us with an appropriate laboratory to study both the complexity out of simple building blocks and simplicity out of the complexity [1]. The low-lying states of nuclei often exhibit a pattern suggestive of symmetries for collective motions (e.g., vibration and rotation). One thus asks to what extent the low-lying states acquire order from the basic properties of interactions (e.g., rotational invariance). This can be studied by permitting the interactions to be more and more arbitrary.In 1998, Johnson, Bertsch, and Dean discovered [2] that spin-zero ground-state (g.s.) dominance in even-even nuclei can be obtained by using random two-body interactions. This result is called the 0-g.s. dominance. Many efforts have been devoted to understand this observation; see Refs. [3-5] for reviews. For recent studies of random Hamiltonians for sd bosons, see Refs. [6][7][8][9][10][11][12].In Ref.[7], Bijker and Frank pointed out that the vibration and rotation are two important motions in sd-boson systems, even if random interactions are assumed. These two motions are characterized by the ratio of the first 4 + state energy with respect to the first 2 + state energy, that is, R 4 = E 4 + 1 /E 2 + 1 (in this paper, we define R I = E I + 1 /E 2 + 1 ). For vibrations R 4 2.0, and for rotations R 4 3.3. The predominance of vibrational and rotational motions is characterized by the sharp peaks in the distribution of R 4 at R 4 2.0 and 3.3.In contrast, the random samples with R 4 = 2.0 or 3.3 have not been paid enough attention to date, because they look like statistical "noise" to the dominant modes (i.e., vibrational and rotational motions) in the two-body random ensemble. There were two studies of R 4 = 2.0 or 3.3: In Ref.[6], Kusnezov and collaborators indicated a pattern of the anharmonic vibrator (AHV) [13] with random interactions, and in Ref.[11], Johnson and Nam noticed the correlation with R I R 4 1 (called the "seniority"-type correlation and denoted by "S" therein), in addition to vibrational and rotational spectra, by the distributions of (R I , R 4 ) for boson number N B = 16.

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confidence: 99%

Correlations of excited states forsdbosons in the presence of random interactions

Lei¹,

Zhao²,

Yoshida³

2011

Phys. Rev. C

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“…Figure 4 shows a few important P (I)'s versus l for four bosons with spin l [50]. One sees that the pattern of I g.s.…”

Section: Bosons With Spin Lmentioning

confidence: 96%

“…For odd n and l = 1, or for n = 3 and any odd l [48], there are no I = 0 states; for odd n and l = 3, 5, 7 and 9, the I = 0 states do not exist unless n ≥ 15, 9, 7, and 5, respectively. For fifteen bosons with l = 3, nine bosons with l = 5, seven bosons with l = 7 and five bosons with l = 9 or 11, P (0) ∼ 0% according to calculations by using 1000 sets of the TBRE Hamiltonian [50]. From Fig.…”

Section: Bosons With Spin Lmentioning

confidence: 99%

“…dominance for four fermions in a single-j shell and four bosons with spin l was recently discussed in Ref. [50]. The essential point is that 6 For fermions in many-j shells, the number of two-body matrix elements is usually large.…”

Section: Fermions In a Single-j Shellmentioning

confidence: 99%

“…An argument why the behavior of the P TBRE (I max , l)'s is different for bosons and fermions, given in Ref. [50], is as follows. As discussed above, the P (I max ) comes essentially from a gap produced by the pairing interaction G Lmax for bosons with spin l, or the pairing interaction G Jmax for fermions in a single-j shell, where L max = 2l and J max = 2j − 1, respectively.…”

Section: Spin I Max Gs Probabilitiesmentioning

confidence: 99%

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Regularities of many-body systems interacting by a two-body random ensemble

Zhao

Arima²,

Yoshinaga

2004

Physics Reports

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The ground states of all even-even nuclei have angular momentum, I, equal to zero, I = 0, and positive parity, π = +. This feature was believed to be a consequence of the attractive short-range interaction between nucleons. However, in the presence of two-body random interactions, the predominance of I π = 0 + ground states (0 g.s.) was found to be robust both for bosons and for an even number of fermions. For simple systems, such as d bosons, sp bosons, sd bosons, and a few fermions in single-j shells for small j, there are a few approaches to predict and/or explain spin I ground state (I g.s.) probabilities. An empirical approach to predict I g.s. probabilities is available for general cases, such as fermions in a single-j (j > 7/2) or many-j shells and various boson systems, but a more fundamental understanding of the robustness of 0 g.s. dominance is still out of reach. Further interesting results are also reviewed concerning other robust phenomena of manybody systems in the presence of random two-body interactions, such as the odd-even staggering of binding energies, generic collectivity, the behavior of average energies, correlations, and regularities of many-body systems interacting by a displaced twobody random ensemble.

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Regularity of atomic nuclei with random interactions: sd bosons

Zhao

2018

Front. Phys.

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Angular momentum distribution of the ground states in the presence of random interactions: Boson systems

Cited by 9 publications

References 27 publications

Correlations of excited states forsdbosons in the presence of random interactions

Correlations of excited states forsdbosons in the presence of random interactions

Regularities of many-body systems interacting by a two-body random ensemble

Regularity of atomic nuclei with random interactions: sd bosons

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