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Chinese Physics C

THE PHASE TRANSITION IN THE TWO-LEVEL PAIRING FORCE R(4)MODEL

Xu G

Published Jan 1, 1986• 0 citations
OpenAlex

Abstract

The phase transition from the super fluid to normal state with the increase of theseniority number in the two-level pairing force model is studied with a boson-fermioncomposite representation. Criteria for identifying the phase transition with observablephase characteristics are discussed.

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Properties of the phase change of the two-level pairing model are investigated in the semi-classical treatment by using the variational approach with a mixed-mode coherent state. In the classical limit, ħ → 0, a sharp phase transition appears, and the two phases exist in the region where the force strength is larger than a certain critical value. However, it is shown that, in the semi-classical treatment, the above-mentioned behavior of the phase change disappears in both analytical and numerical treatments. This leads to a new understanding of the properties of the phase change in this model.
Aspects of the phase change of the two-level pairing model are investigated in the semi-classical treatment by using the variational approch with the mixed-mode coherent state. In the classical limit, � → 0, the sharp phase transition appears and the two phases exist in the region where the force strength is larger than a certain critical value. However, it is shown that, in the semi-classical treatment, the abovementioned behavior of the phase change disappears in the analytical and the numerical treatments. As a result, new understanding about aspects of the phase change in this model is given. The phase structure and the phase transitions between various phases in condensed matter systems, such as nuclear and/or quark matter as well as the condensed matter in atoms and molecules, are important concepts to understand the nature of the matter under consideration. In the infinite systems, the clear phase separation is often realized and, in that
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.