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首页> 外文期刊>Nuclear Physics, A: Journal Devoted to the Experimental Study of the Fundamental Constituents of Matter and Their Actions >Phase transitions and quasi-dynamical symmetry in nuclear collective models, III: The U(5) to SU(3) phase transition in the IBM
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Phase transitions and quasi-dynamical symmetry in nuclear collective models, III: The U(5) to SU(3) phase transition in the IBM

机译：核集体模型中的相变和准动力学对称，III：IBM中的U（5）到SU（3）相变

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This paper studies the dependence of the U(5) to SU(3) phase transition in the interacting boson model (IBM) on the finite number N of bosons. Such investigations illuminate the relationship between a first order transition in a macroscopic system, which exhibits a discontinuous change of some of its properties at a highly singular critical point, and a transition in a corresponding finite particle system, which shows a critical point smeared by fluctuations. The IBM model Hamiltonian H(alpha) = (I - alpha)H-1 + alpha H-2 of this paper is an interpolation between a U(5)-invariant Hamiltonian H-1, given by the d-boson number operator, and an SU(3) Hamiltonian H-2, given by a quadrupole-quadrupole operator. For N sufficiently large, the low energy eigenstates of H(alpha) fall into either a U(5) phase or an SU(3) phase depending on the value of alpha. An exception is a narrow zone around a critical value of alpha. The width of this critical zone decreases as N increases. In this zone the spectra for the N values considered show an approximate X(5) dynamical symmetry to within an N-dependent scale factor. The states in the SU(3) phase show an SU(3) quasi-dynamical symmetry that becomes more well-defined as N increases. The states in the U(5) phase show a U(5) quasi-dynamical symmetry albeit one that closely approaches a pure U(5) dynamical symmetry for smaller values of alpha and which also becomes better defined the larger the particle number. The concluding section reviews studies of phase transitions in nuclear physics. (c) 2005 Elsevier B.V. All rights reserved.
机译：本文研究了玻色子相互作用模型（IBM）中U（5）到SU（3）相变对有限数量N玻色子的依赖性。这样的研究阐明了宏观系统中的一阶跃迁与相应有限粒子系统中的跃迁之间的关系，其中一阶跃迁在高度奇异的临界点处表现出其某些特性的不连续变化，而该相变表示了由于波动而模糊的临界点。 。本文的IBM模型哈密顿量H（alpha）=（I-α）H-1 +αH-2是d玻色子数算子给出的U（5）不变哈密顿量H-1之间的插值，由四极-四极算子给出的SU（3）哈密顿H-2。对于足够大的N，取决于α的值，Hα的低能本征态分为U（5）相或SU（3）相。一个例外是alpha临界值附近的狭窄区域。临界区的宽度随着N的增加而减小。在该区域中，所考虑的N值的光谱在N依赖的比例因子内显示出近似的X（5）动态对称性。 SU（3）相中的状态显示SU（3）准动力学对称性，随着N的增加，它变得更加清晰。 U（5）阶段的状态显示了U（5）准动态对称性，尽管对于较小的α值而言，它接近逼近纯U（5）动力学对称性，并且随着粒子数的增加，它也变得更好地定义了。结论部分回顾了核物理中相变的研究。 （c）2005 Elsevier B.V.保留所有权利。

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