Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Quantum Phase Transition for γ -Soft Nuclei

Jan Jolie, Richard F. Casten, Peter von Brentano, Volker Werner

Published Oct 2, 2001• 156 citations
Publisher

Abstract

We examine a quantum phase transition in $\ensuremath{\gamma}$-soft nuclei, where the O(6) limit is simultaneously a dynamical symmetry of the U(6) group of the interacting boson model and a critical point of a prolate-oblate phase transition. This is the only example of phase transitional behavior that can be described analytically for a finite $s,d$ boson system.

DOI
10.1103/physrevlett.87.162501

Related papers

Quantum Phase Transition for gamma-Soft Nuclei

Richard F. Casten, Jan Jolie, Peter von Brentano +1 more

We examine a quantum phase transition in gamma-soft nuclei, where the O(6) limit is simultaneously a dynamical symmetry of the U(6) group of the interacting boson model and a critical point of a prolate-oblate phase transition. This is the only example of phase transitional behavior that can be described analytically for a finite s,d boson system.

Physical Review Letters•Jan 1, 2001•72 citations

The prolate-oblate shape phase transition in the interacting boson model

Yu Zhang, J. Xu, Si-Han Li +1 more

The prolate-oblate shape phase transition in the the interacting boson model is revisited by adopting the transitional Hamiltonian with a linear dependence on the control parameter. The analysis of the shape phase transition in both the large-N limit and finite N case shows that the O(6) symmetry is robust as the critical point symmetry of the prolate-oblate shape phase transition.

EPJ Web of Conferences•Jan 1, 2013•2 citations

Critical-Point Structure in Finite Nuclei

A. Leviatan

Properties of quantum shape‐phase transitions in finite nuclei are considered in the framework of the interacting boson model. Special emphasis is paid to the dynamics at the critical‐point of a general first‐order phase transition.

arXiv:nucl-th/0612015•AIP conference proceedings•Jan 1, 2006•0 citations

Quantum phase transition in the U(4) vibron model and the E(3) symmetry

Yu Zhang, Zhanfeng Hou, Huan Chen +2 more

We study the details of the U(3)--O(4) quantum phase transition in the U(4) vibron model. Both asymptotic analysis in the classical limit and rigorous calculations for finite boson number systems indicate that a second-order phase transition is still there even for the systems with boson number $N$ ranging from tens to hundreds. Two kinds of effective order parameters, including $E1$ transition ratios $B(E1:{2}_{1}\ensuremath{\rightarrow}{1}_{1})/B(E1:{1}_{1}\ensuremath{\rightarrow}{0}_{1})$ and $B(E1:{0}_{2}\ensuremath{\rightarrow}{1}_{1})/B(E1:{1}_{1}\ensuremath{\rightarrow}{0}_{1})$, and the energy ratios ${E}_{{2}_{1}}/{E}_{{0}_{2}}$ and ${E}_{{3}_{1}}/{E}_{{0}_{2}}$ are proposed to identify the second-order phase transition in experiments. We also found that the critical point of phase transition can be approximately described by the E(3) symmetry, which persists even for moderate $N~10$ protected by the scaling behaviors of quantities at the critical point. In addition, a possible empirical example exhibiting roughly the E(3) symmetry is discussed.

Physical Review C•Aug 25, 2008•26 citations

Prolate–oblate quantum phase transition in odd nuclei for $$j = 1/2, 3/2$$ and 5/2 orbits within the $$SU^{BF}(3)$$ limit of the IBFM

Z. Ranjbar, L. Fortunato, Nader Ghahramany

The European Physical Journal Plus•Oct 21, 2022•0 citations

Quantum phase transitions in the consistent-QHamiltonian of the interacting boson model

Feng Pan, Tao Wang, Yukun Huo +1 more

Quantum phase transitional patterns in the whole parameter space of the consistent- Q Hamiltonian in the interacting boson model are studied based on an implemented Fortran code for the numerical computation of the matrix elements in the SU (3) Draayer–Akiyama basis. Results with respect to both ground and some excited states of the model Hamiltonian are discussed. Quantum phase transitional behavior in a variety of parameter situations is shown. It is found that transitional behavior of excited states is more complicated. Pt isotopes are taken as examples in illustrating the prolate–oblate shape phase transition.

Journal of Physics G Nuclear and Particle Physics•Oct 3, 2008•34 citations
We examine a quantum phase transition in \ensuremathγ\ensuremath{\gamma}\ensuremathγ-soft nuclei, where the O(6) limit is simultaneously a dynamical symmetry of the U(6) group of the interacting boson model and a critical point of a prolate-oblate phase transition. This is the only example of phase transitional behavior that can be described analytically for a finite s,ds,ds,d boson system.
We study the details of the U(3)--O(4) quantum phase transition in the U(4) vibron model. Both asymptotic analysis in the classical limit and rigorous calculations for finite boson number systems indicate that a second-order phase transition is still there even for the systems with boson number NNN ranging from tens to hundreds. Two kinds of effective order parameters, including E1E1E1 transition ratios $B(E1:{2}_{1}\ensuremath{\rightarrow}{1}_{1})/B(E1:{1}_{1}\ensuremath{\rightarrow}{0}_{1})$ and $B(E1:{0}_{2}\ensuremath{\rightarrow}{1}_{1})/B(E1:{1}_{1}\ensuremath{\rightarrow}{0}_{1})$, and the energy ratios E21/E02{E}_{{2}_{1}}/{E}_{{0}_{2}}E21​​/E02​​ and E31/E02{E}_{{3}_{1}}/{E}_{{0}_{2}}E31​​/E02​​ are proposed to identify the second-order phase transition in experiments. We also found that the critical point of phase transition can be approximately described by the E(3) symmetry, which persists even for moderate N 10N~10N 10 protected by the scaling behaviors of quantities at the critical point. In addition, a possible empirical example exhibiting roughly the E(3) symmetry is discussed.
Prolate–oblate quantum phase transition in odd nuclei for j=1/2,3/2j = 1/2, 3/2j=1/2,3/2 and 5/2 orbits within the SUBF(3)SU^{BF}(3)SUBF(3) limit of the IBFM
Quantum phase transitional patterns in the whole parameter space of the consistent- Q Hamiltonian in the interacting boson model are studied based on an implemented Fortran code for the numerical computation of the matrix elements in the SU (3) Draayer–Akiyama basis. Results with respect to both ground and some excited states of the model Hamiltonian are discussed. Quantum phase transitional behavior in a variety of parameter situations is shown. It is found that transitional behavior of excited states is more complicated. Pt isotopes are taken as examples in illustrating the prolate–oblate shape phase transition.