Chaotic dynamics in collective models of nuclei

Stránský, Pavel; Macek, Michal; Cejnar, Pavel; Frank, A.; Fossión, Rubén; Landa, Emmanuel

doi:10.1088/1742-6596/239/1/012002

Cited by 4 publications

(5 citation statements)

References 15 publications

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“…As shown in [17,23], the classical Bohr Hamiltonian exhibits a very sophisticated interplay of regular and chaotic features. This also quantified its quantized version to be used in numerous theoretical analyzes related to quantum chaos [24][25][26][27][28][29].…”

Section: Test In the Bohr Modelmentioning

confidence: 99%

Study of a curvature-based criterion for chaos in Hamiltonian systems with two degrees of freedom

Stránský¹,

Cejnar²

2015

J. Phys. A: Math. Theor.

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A non-Euclidean geometric criterion for chaos (Horwitz et al 2007 Phys. Rev. Lett. 98 234301) is investigated in bound systems with two degrees of freedom. It is shown that the criterion is partly equivalent to a simpler indicator of chaos based on the shape of equipotential curves. The method is numerically tested in a restricted Bohr model and in an extended Creagh-Whelan model. Although in some cases the geometric criterion approximately predicts the onset of chaos at low energies, manifest counterexamples disproving its general applicability are demonstrated.

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Section: Test In the Bohr Modelmentioning

confidence: 99%

Study of a curvature-based criterion for chaos in Hamiltonian systems with two degrees of freedom

Stránský¹,

Cejnar²

2015

J. Phys. A: Math. Theor.

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“…Is the classical map in Figure 2 doubled by a similar quantum picture based on statistical properties of quantal spectra? The answer is yes [11,12]. The analysis preceding this conclusion took into account both short-and long-range spectral correlations (statistical distributions of the intervals between neighboring and distant levels) and was performed for various values of the mass parameter M (changeable level densities) and different quantized versions of the model for T rot ¼ 0.…”

Section: Quantum Chaos: a Visual Approachmentioning

confidence: 99%

“…This may lead to an impression that the collective modes of nuclei are mostly regular. However, detailed studies performed in both the IBM [7][8][9] and GCM [10][11][12] show that collective dynamics in between the dynamically symmetric cases exhibits a rather complicated interplay between order and chaos. The coexistence of simple and complex features disclosed in these studies makes the collective nuclear models an excellent theoretical laboratory which in many respects surpasses the quantum billiards mentioned earlier.…”

Section: Introductionmentioning

confidence: 99%

Regular and Chaotic Collective Modes in Nuclei

Cejnar

Stránský

Macek

2011

Nuclear Physics News

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IntroductionAtomic nuclei constitute an exemplary realization of chaotic dynamics in the quantum domain. These dense clouds of strongly interacting particles were at the dawn of the field of physics called quantum chaos [1,2]. In the 1980s, when its fundamentals were formulated, the field might be seen just as an exotic branch of quantum mechanics, but the present rapid growth of "quantum technologies" gives it a more practical potential.Paradoxically, the most difficult task of "quantum chaos" is to find what this term actually means. It is clear that the classical definition of chaos based on an extreme sensitivity of the motion to initial conditions (exponential divergence of trajectories, or the "butterflywing effect") cannot be applied in quantum mechanics due to linearity of the Schrödinger equation. Instead, distinct signatures of chaos in bound quantum systems lie in statistical properties of discrete energy spectra. More specifically, the systems having chaotic classical counterparts were found [3] to exhibit strong correlations between energy levels across the whole spectrum-correlations that are consistent with the theory of random matrices, originally proposed in the 1950s for the description of slow neutron resonances in nuclei [4]. This connection, which also leads to important dynamical consequences, has been tested in several schematic models, particularly in two-dimensional cavities, so-called "billiards," with shapes generating different proportions of regular and chaotic classical motions [1,2].Nuclei also exhibit rather well-pronounced collective motions-coherent rotations or vibrations of a large number of nucleons. These motions are well described by models far simpler than those considering all the microscopic degrees of freedom. Both generally accepted representatives of such

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“…It can be obtained either from an expansion of scalars constructed from the quadrupole deformation parameters [3], or from a particular quadrupole boson Hamiltonian by the use of the time-dependent variational principle and coherent states [5]. It was shown that the GCM exhibits rich interplay of regularity and chaos, and its properties were studied both in the classical case [6][7][8][9][10] and in the quantum case [7,[11][12][13][14]. The well-described diversity of the dynamics predestines the model for testing new theoretical approaches to chaos.…”

Section: Introductionmentioning

confidence: 99%

Geometric criterion for chaos in collective dynamics of nuclei

Stránský¹,

Cejnar²

2015

Phys. Scr.

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A local geometrical criterion for chaos, based on an embedding of a Hamiltonian system into an appropriately chosen curved space, is applied in the classical version of the Geometric Collective Model of nuclei. The criterion is shown to be equivalent with a simpler indicator of chaos based on the convex-concave change of equipotential curves. It is tested by comparing its predictions with a detailed numerical analysis of global dynamics. The results indicate a capacity of the method to estimate the energy of the onset of chaos, but also demonstrate convincing counterexamples that disprove its general applicability.

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Chaotic dynamics in collective models of nuclei

Cited by 4 publications

References 15 publications

Study of a curvature-based criterion for chaos in Hamiltonian systems with two degrees of freedom

Study of a curvature-based criterion for chaos in Hamiltonian systems with two degrees of freedom

Regular and Chaotic Collective Modes in Nuclei

Geometric criterion for chaos in collective dynamics of nuclei

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