Regular spectra in the vibron model with random interactions

Bijker, R.; Frank, A.

doi:10.1103/physrevc.65.044316

Cited by 31 publications

(36 citation statements)

References 27 publications

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“…For this reason, the Hamiltonian effectively depends on two random coefficients cos χ and sin χ , which can be either attractive or repulsive. The distribution of ground state angular momenta was obtained exactly in a mean-field study [17]. For even values of the number of bosons N , the ground state has v = 0 in 75% of the cases and v = N in the remaining 25 %.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…Despite the progress and new insights in understanding the appearance of ordered spectra from random interactions, the proposed explanations offer partial solutions of the problem, without being able to account for all observed regular phenomena in systems of randomly interacting fermions and bosons. Among others, we mention induced pairing [15], geometric chaoticity for randomly interacting fermions [7,16], mean-field analysis for the interacting boson model and the vibron model [17], spectral widths [10,18], and an empirical method based on the eigenvalues of each independent two-body matrix element [12].…”

Section: Introductionmentioning

confidence: 99%

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Eigenvalue correlations and the distribution of ground state angular momenta for random many-body quantum systems

2009

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The observed preponderance of ground states with angular momentum L = 0 in many-body quantum systems with random two-body interactions is analyzed in terms of correlation coefficients (covariances) among different eigenstates. It is shown that the geometric analysis of Chau et al. can be interpreted in terms of correlations (covariances) between energy eigenvalues, thus providing an entirely statistical explanation of the distribution of ground state angular momenta of randomly interacting quantum systems that, in principle, is valid for both fermionic and bosonic systems. The method is illustrated for the interacting boson model.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Eigenvalue correlations and the distribution of ground state angular momenta for random many-body quantum systems

2009

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“…When one applies the TBRE Hamiltonian to sp bosons [51,52], sd bosons [16,17,51,53,54,55,56,57], and sdg [58] bosons (we shall come to these cases in subsections 4.6 and 5.2), the 0 g.s. dominance is found also for an odd number of bosons.…”

Section: Bosons With Spin Lmentioning

confidence: 99%

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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“…Group theory was used to show that the TBRE on a single j shell had a particular group symmetry and "this gave rise to the simplicity in the ground state structures" [16]. A Hartree-Fock calculation in the IBM and vibron model showed that there are 3 equilibrium shapes that explain the rotational bands and J0D [6,17,18]. An expression for the energy gap in the lowest spin states in the TBRE was found in [19].…”

Section: Explanationsmentioning

confidence: 99%

Randomly interacting bosons on two spin levels

Mulhall¹

2017

AIP Conference Proceedings

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Abstract. 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 ∆ 3 statistic.

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Regular spectra in the vibron model with random interactions

Cited by 31 publications

References 27 publications

Eigenvalue correlations and the distribution of ground state angular momenta for random many-body quantum systems

Eigenvalue correlations and the distribution of ground state angular momenta for random many-body quantum systems

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

Randomly interacting bosons on two spin levels

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