Regularity and chaos in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>0</mml:mn><mml:mo>+</mml:mo></mml:msup></mml:math>states of the interacting boson model using quantum measures

Karampagia, S.; Bonatsos, Dennis; Casten, R. F.

doi:10.1103/physrevc.91.054325

Cited by 15 publications

(31 citation statements)

References 58 publications

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“…However, it has been known for many years that there exists a chaotic region in the SU(3)-SO(6) transitional region [30,31,33,35], which in turn suggests that there may exist the SU(3)-SO(6) ESQPTs occurring in this transitional region according to the previous analysis. In order to verify the ESQPTs, the lowest 124 levels with L = 0 as functions of the control parameter χ obtained from (1) with η = 1 are shown in Fig.…”

Section: The Su(3)-so(6) Esqptmentioning

confidence: 96%

“…On the other hand, it has been revealed that there exists a chaotic region within the U(5)-SU(3) transitional region [30][31][32][33], where the spectral statistics with a fixed angular momentum such as L = 0 indicate strong chaos [33]. The range of the chaotic region may lie between the critical point and the SU(3) limit, where the U(5)-SU(3) ESQPT also occurs as shown in Fig.…”

Section: B the U(5)-su(3) Esqptmentioning

confidence: 99%

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Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of0+states and effective order parameter

2016

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The spectral characteristics of the L π = 0 + excited-states in the interacting boson model are systematically investigated. It is found that various types of excited-state quantum phase transitions may widely occur in the model as functions of the excitation energy, which indicates that the phase diagram of the interacting boson model can be dynamically extended along the direction of the excitation energy. It has also been justified that the d-boson occupation probability ρ(E) is qualified to be taken as the effective order parameter to identify these excited-state quantum phase transitions. In addition, the underlying relation between the excite-state quantum phase transition and the chaotic dynamics is also stated.

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Section: The Su(3)-so(6) Esqptmentioning

confidence: 96%

Section: B the U(5)-su(3) Esqptmentioning

confidence: 99%

Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of0+states and effective order parameter

2016

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“…In Refs. 63 – 67 , Macek et al, suggested the rotational bands as the results of an adiabatic separation of collective rotations built upon a subset of intrinsic vibrational states IBM framework. They offer regularity to intrinsic vibrational mode versus chaoticity, which yields due to collective rotations.…”

Section: Resultsmentioning

confidence: 99%

Partial dynamical symmetry versus quasi dynamical symmetry examination within a quantum chaos analyses of spectral data for even–even nuclei

Sabri

Mobarakeh

Majarshin

et al. 2021

Sci Rep

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Statistical analyses of the spectral distributions of rotational bands in 51 deformed prolate even–even nuclei in the 152 ≤ A ≤ 250 mass region $$R_{{4_{1}^{ + } /2_{1}^{ + } }} \ge 3.00$$ R 4 1 + / 2 1 + ≥ 3.00 are examined in terms of nearest neighbor spacing distributions. Specifically, the focus is on data for 0+, 2+, and 4+ energy levels of the ground, gamma, and beta bands. The chaotic behavior of the gamma band, especially the position of the $$2_{\gamma }^{ + }$$ 2 γ + band-head compared to other levels and bands, is clear. The levels are analyzed within the framework of two models, namely, a SU(3)-partial dynamical symmetry Hamiltonian and a SU(3) two-coupled quasi-dynamical symmetry Hamiltonian, with results that are further analyzed using random matrix theory. The partial and quasi dynamics both yield outcomes that are in reasonable agreement with the known experimental results. However, due to the degeneracy of the beta and gamma bands within the simplest SU(3) picture, the theory cannot be used to describe the fluctuation properties of excited bands. By changing relative weights of the different terms in the partial and quasi dynamical Hamiltonians, results are obtained that show more GOE-like statistics in the partial dynamical formalism as the strength of the pairing term is increased. Also, in the quasi-dynamical symmetry limit, more correlations are found because of the stronger couplings.

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“…A fascinating point of this arc is that its parameter trajectory may point to a very chaotic situation with the Hamiltonian mixing the U(5), O (6) and SU(3) dynamical symmetries. However, the statistical analysis [8,10] indicate that the spectra associated with the entire AW arc are unexpected regular (especially in a large N case [14]) in contrast to its adjacent parameter area. The AW arc has been extensively studied from different angles [15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 95%

“…It is remained to answer whether or not the statistical results themselves can be taken as a criterion of distinguishing the excited states. In fact, an analysis of the energy dependence of the spectral fluctuations has already been given in [14] but the study focuses on the cases in the vicinity of the AW arc with only the states of zero spin being discussed. In this work, we hope to give a more general examination of the energy dependence of spectral fluctuations in the IBM to reveal the possible connections between spectral fluctuations and mean-field structures.…”

Section: Introductionmentioning

confidence: 99%

Spectral fluctuations in the interacting boson model*

Wu¹,

Teng²,

Hou³

et al. 2022

Chinese Phys. C

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The energy dependence of the spectral fluctuations in the interacting boson model (IBM) and its connections to the mean-field structures have been analyzed through adopting two statistical measures, the nearest neighbor level spacing distribution $P(S)$ measuring the chaoticity (regularity) in energy spectra and the $\Delta_3(L)$ statistics of Dyson and Metha measuring the spectral rigidity. Specifically, the statistical results as functions of the energy cutoff have been worked out for different dynamical situations including the U(5)-SU(3) and SU(3)-O(6) transitions as well as those near the AW arc of regularity. It is found that most of the changes in spectral fluctuations are triggered near the stationary points of the classical potential especially for the cases in the deformed region of the IBM phase diagram. The results thus justify the stationary point effects from the point of view of statistics. In addition, the approximate degeneracies in the $2^+$ spectrum on the AW arc is also revealed from the statistical calculations.

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Regularity and chaos in0+states of the interacting boson model using quantum measures

Cited by 15 publications

References 58 publications

Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of0+states and effective order parameter

Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of0+states and effective order parameter

Partial dynamical symmetry versus quasi dynamical symmetry examination within a quantum chaos analyses of spectral data for even–even nuclei

Spectral fluctuations in the interacting boson model*

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