Chaos in the low-lying collective states of even-even nuclei

Alhassid, Y.; Novoselsky, A.; Whelan, Niall D.

doi:10.1103/physrevlett.65.2971

Cited by 92 publications

(94 citation statements)

References 13 publications

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“…We note that this result is in accordance with the general considerations of Zhang et al [38][39][40] stating that chaotic motion can be considered as being associated with breaking of the dynamical symmetry 9 It agrees also with the recent work of Alhassid et al [23,24] who investigated the breaking of the SU(3) symmetry within the IBM. In [23,24], however, the S U(6) symmetry has been kept intact, while in the present investigation -by introducing the truncation parameter u -also the S U(6) symmetry is broken.…”

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confidence: 91%

Level density fluctuations in the generalized interacting boson model

Lopac

Paar

1992

Z. Physik A - Hadrons and Nuclei

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Abstract. Level density fluctuations are calculated within the generalized interacting boson model proposed for even-even nuclei, in dependence on the truncation parameter ~c. For the case z=2 corresponding to the SU(3) dynamical symmetry of the interacting boson model the fluctuation pattern is close to Poissonian. For cases z r 2, including the anharmonic vibrator model for which z = oo, a rapid transition to the fluctuation pattern close to GOE is obtained. PACS: 24.60.Ky; 21.60.Ev; 21.60.Fw Fluctuations of the energy level density in quantum systems have received much attention in recent years [1][2][3]. This interest is mostly due to the conjecture expressed by Bohigas et al. [4] stating that the distribution of the level spacings within the quantum energy spectrum reflects the nature of the corresponding classical system. According to this conjecture, the systems exhibiting the regular behaviour in the classical limit, have the Poissonian distribution of the quantum energy levels, and the quantum systems whose classical counterparts behave chaotically conform to the Gaussian orthogonal ensemble (GOE, Wigner) type of the level spacing distribution.A number of recent investigations made it clear that there are many quantum systems which belong to the intermediate class, exhibiting a pattern lying between the two limits [3,5,6]. The importance of an interaction parameter controlling the transition between Poisson and GOE limits has been stressed in different contexts [7,8]. It has also been emphasized that the absence of the coupling results in a high degree of degeneracy and leads to a pattern exceeding the values of the Poisson limit [9,10].All of the mentioned features are typical also for the nuclear spectra [11]. The transition from regularity to chaos -in the sense of the conjecture of Bohigas et al. -has been clearly identified both in the experimental level spacings [12][13][14][15][16] and in the model calculations for the realistic nuclei [17][18][19][20][21][22][23][24][25][26][27]. It can be summarized in the statement that the realistic nuclear spectra are intermediate between Poisson and GOE type of fluctuations, showing the tendency to be closer to the GOE limit. The role of collectivity in this tendency is currently being investigated.In the present paper we investigate the level density fluctuations of spectra for even-even nuclear systems described by the generalized interacting boson model (generalized truncated quadrupole-boson model), which will be referred to as the GTQM model. The GTQM Hamiltonian in the quadrupole boson representation reads , h4L[(b + b2+)L(s163 9 L=0,2,4 (1)Here, b+u and b2u denote the creation and annihilation operators, respectively, of the quadrupole bosons, Ho=hlN. These can be denoted as INvI) where N is the quadrupole boson number, I stands for the angular momentum and v is an additional quantum number necessary in some cases to distinguish between the states of the same/. We consider the truncation function operator f (N) defined as

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confidence: 91%

Level density fluctuations in the generalized interacting boson model

Lopac

Paar

1992

Z. Physik A - Hadrons and Nuclei

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“…Though the phase diagram of this st model and the QCH coincide in the large N limit, beyond the mean-field level the QCH may have different properties due to the dynamics of fluctuations and correlations in the full (β, γ ) space [21][22][23]. In particular, while our st model is fully integrable [24] the IBM is chaotic for χ = 0 [25] with the exception of the SU(3) symmetry limit. Extension of the formalism presented in this paper to the IBM will be the subject of a forthcoming publication [17].…”

Section: Discussionmentioning

confidence: 99%

Scalar two-level boson model to study the interacting boson model phase diagram in the Casten triangle

et al. 2006

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“…In their remarkable series of works [18,16,19,20,17], Alhassid, Whelan, and Novoselsky mapped the classical and quantum signatures of chaos associated with the hamiltonian (4) in the whole (η,χ)-parameter range for various angular momenta. As shown in a recent work [15], the observed behaviour of standard chaotic measures has a counterpart in the behaviour of the entropy-ratio product R from Eq.…”

Section: Resultsmentioning

confidence: 99%

“…Chaotic properties of a specific two-parameter set of IBM-1 hamiltonians were throughoutly studied by Alhassid, Whelan, and Novoselsky [16][17][18][19][20]. As we follow the cited works in order to relate the order/chaos signatures to the dynamical-symmetry content, we use the same parameterization of the IBM-1 hamiltonian.…”

Section: Casten Trianglementioning

confidence: 99%

Wave-function entropy and dynamical symmetry breaking in the interacting boson model

Cejnar

Jolie

1998

Phys. Rev. E

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The degree of chaos in the Interacting Boson Model (IBM-1) is compared with what we call the "dynamical-symmetry content" of the system. The latter is represented by the information entropy of the eigenfunctions with respect to bases associated with dynamical symmetries of the IBM-1, and expresses thus the localization of actual eigenfunctions in these symmetry bases.The wave-function entropy is shown to be a sensitive tool for monitoring the processes of a single dynamical-symmetry breaking or transitions between two and more symmetries. For the IBM-1 hamiltonians studied here, the known features related to chaos, namely the dependence of chaotic measures on the hamiltonian parameters (position in the Casten triangle) and on the angular momentum, turn out to be correlated with the behaviour of the wave-function entropy.21.60.Fw; 05.45.+b Typeset using REVT E X 1

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Chaos in the low-lying collective states of even-even nuclei

Cited by 92 publications

References 13 publications

Level density fluctuations in the generalized interacting boson model

Level density fluctuations in the generalized interacting boson model

Scalar two-level boson model to study the interacting boson model phase diagram in the Casten triangle

Wave-function entropy and dynamical symmetry breaking in the interacting boson model

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