Chaotic properties of the interacting boson model

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

“…(13), uses an approximation (the replacement of the quadrupole operator by the intrinsic quadrupole moment), which cannot be tested separately for each state. The same holds for the work of Alhassid and Whelan [2,3], leading to the regular region approximated [6] by Eq. (14).…”

“…degeneracy in the IBA framework leads to a line inside the symmetry triangle of the IBA which, in the region between the SU(3) vertex and the shape/phase coexistence region [10] (separating spherical from prolate deformed shapes), is located very close to the arc of regularity, while at the same time the degeneracies predicted by SU (3), not only for the β 1 and γ 1 bands, but also for bands belonging to higher irreducible representations (irreps) of SU (3), are preserved to a very good extent [9]. This result extends the notion of quasidynamical symmetry (QDS), originally introduced [11,12,13,14,15] for describing the persistence of limiting symmetries along the U(5)-O(6) and U(5)-SU(3) legs of the IBA, to the interior of the triangle.…”

“…The study of chaotic properties of the Interacting Boson Approximation (IBA) model [1], both classically and quantum mechanically, led to the discovery [2,3] of a narrow strip of nearly regular behavior inside the symmetry triangle [4] of the IBA, connecting the U(5) and SU (3) limiting symmetries, in addition to the regular region along the U(5)-O(6) leg of the triangle.…”

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

“…Thus, one may conclude that the chaotic behavior of the spectrum in the U(5)-SU(3) transitional region might be due to the spectrum involving these two different types of excited states simultaneously. Although the similar situation may also occur in the U(5)-SO(6) ESQPT region, the level statistics in the whole U(5)-SO(6) region is always regular just due to the common SO(5) sub-symmetry [30][31][32].…”

“…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.…”