Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

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

doi:10.1103/physrevc.83.054313

Cited by 8 publications

(24 citation statements)

References 50 publications

(152 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While the fluctuation measures of chaos reveal semiregularity on the arc, they cannot reveal the nature of the approximate symmetry underlying the Alhassid-Whelan arc of regularity, a question which has been addressed in several recent studies [24,26,28,29], but still remains open.…”

Section: Discussionmentioning

confidence: 99%

“…1, namely on the SU(3) vertex, a point on the arc of regularity having parameters (η, χ) = (0.632, −0.803) and at two points with the same η lying off the arc at (η, χ) = (0.632, −0.7) and (η, χ) = (0.632, −1.1). The value η = 0.632 corresponds to ζ = 0.7 in a different parametrization [29], and was chosen in order to be in accordance with the value used in Ref. [28].…”

Section: A Quantum Chaotic Dynamics Of 0 + Statesmentioning

confidence: 99%

See 1 more Smart Citation

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

2015

Self Cite

View full text Add to dashboard Cite

Background: Statistical measures of chaos have long been used in the study of chaotic dynamics in the framework of the interacting boson model. The use of large number of bosons renders additional studies of chaos possible, that can provide a direct comparison with similar classical studies of chaos.Purpose: We intend to provide complete quantum chaotic dynamics at zero angular momentum in the vicinity of the arc of regularity and link the results of the study of chaos using statistical measures with those of the study of chaos using classical measures.Method: Statistical measures of chaos are applied on the spectrum and the transition intensities of 0 + states in the framework of the interacting boson model.Results: The energy dependence of chaos is provided for the first time using statistical measures of chaos. The position of the arc of regularity was also found to be stable in the limit of large boson numbers.Conclusions: The results of the study of chaos using statistical measures are consistent with previous studies using classical measures of chaos, as well as with studies using statistical measures of chaos, but for small number of bosons and states with angular momentum greater than 2.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: A Quantum Chaotic Dynamics Of 0 + Statesmentioning

confidence: 99%

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

2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…A formal justification for this replacement is given in Ref. [4], where matrix elements of the commutators of the relevant parts of the Hamiltonian with the quadrupole operator are properly considered, resulting in the appearance of the intrinsic quadrupole moment.…”

Section: Group Contractionsmentioning

confidence: 99%

“…The first contraction has been used in Ref. [4] for determining a line of approximate SU(3) symmetry inside the symmetry triangle of the IBA, as described by S. Karampagia in this conference [7].…”

Section: Group Contractionsmentioning

confidence: 99%

Group contractions and conformal maps in nuclear structure models

Bonatsos¹

2019

hnps

Self Cite

View full text Add to dashboard Cite

Group contraction is a procedure in which a symmetry group is reduced into a group of lower symmetry in a certain limiting case. Examples are provided in the large boson mumber limit of the Interacting Boson Approximation (IBA) model by a) the contraction of the SU(3) algebra into the [R5]SO(3) algebra of the rigid rotator, consisting of the angular momentum operators forming SO(3), plus 5 mutually commuting quantities, the quadrupole operators, b) the contraction of the O(6) algebra into the [R5]SO(5) algebra of the ∞-unstable rotator. We show how contrac- tions can be used for constructing symmetry lines in the interior of the symmetry triangle of the IBA model. In mathematics, a conformal map is a function which preserves angles. We show how this procedure can be used in the framework of the Bohr Hamiltonian, leading to a Hamiltonian in a curved space, in which the mass depends on the nuclear deformation Ø, while it remains independent of the collective variable ∞ and the three Euler angles. This Hamiltonian is proved to be equivalent to that obtained using techniques of Supersymmetric Quantum Mechanics.

show abstract

“…The conclusions are presented in Section 4. Necessary commutation relations and matrix elements for the calculations are given in the Appendices of [1].…”

Section: Introductionmentioning

confidence: 99%

Line of approximate SU(3) symmetry inside the symmetry triangle of the Interacting Boson Model

Bonatsos¹,

Karampagia²,

Casten³

2020

hnps

Self Cite

View full text Add to dashboard Cite

The U(5), SU(3), and O(6) symmetries of the Interacting Boson Model (IBM) have been traditionally placed at the vertices of the symmetry triangle, while an O(5) symmetry is known to hold along the U(5)–O(6) side of the triangle. We construct [1] for the first time a symmetry line in the interior of the triangle, along which the SU(3) symmetry is preserved. This is achieved by using the contraction of the SU(3) algebra to the algebra of the rigid rotator in the large boson number limit of the IBM. The line extends from the SU(3) vertex to near the critical line of the first order shape/phase transition separating the spherical and prolate deformed phases. It lies within the Alhassid–Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices amidst chaotic regions, thus providing an explanation for its existence.

show abstract

Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

Cited by 8 publications

References 50 publications

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

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

Group contractions and conformal maps in nuclear structure models

Line of approximate SU(3) symmetry inside the symmetry triangle of the Interacting Boson Model

Contact Info

Product

Resources

About