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Pan, F; Zhang, YZ; Draayer, JP; Zhang, YZ (reprint author), Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia.; Zhang, YZ (reprint author), Chinese Acad Sci, CAS Key Lab Theoret Phys, Inst Theoret Phys, Beijing 100190, Peoples R China. | |
Exact solution of the two-axis countertwisting hamiltonian for the half-integer J case | |
Source Publication | JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT |
Language | 英语 |
Keyword | Quantum Integrability (Bethe Ansatz) |
Abstract | Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) J are derived based on the Jordan-Schwinger (differential) boson realization of the SU(2) algebra after desired Euler rotations, where J is the total angular momentum quantum number of the system. It is shown that solutions to the Bethe ansatz equations can be obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of solutions, with solution number being J + 1 and J respectively when J is an integer and J + 1/2 each when J is a half-integer, are obtained. Properties of the zeros of the related extended Heine-Stieltjes polynomials for half-integer J cases are discussed. It is clearly shown that double degenerate level energies for half-integer J are symmetric with respect to the E = 0 axis. It is also shown that the excitation energies of the 'yrast' and other 'yrare' bands can all be asymptotically given by quadratic functions of J, especially when J is large. |
2017 | |
Pages | 23104 |
Subject Area | Mechanics ; Physics |
DOI | http://dx.doi.org/10.1088/1742-5468/aa5a28 |
Funding Organization | US National Science Foundation [OCI-0904874, ACI-1516338] ; US National Science Foundation [OCI-0904874, ACI-1516338] ; US National Science Foundation [OCI-0904874, ACI-1516338] ; US National Science Foundation [OCI-0904874, ACI-1516338] ; US Department of Energy [DE-SC0005248] ; US Department of Energy [DE-SC0005248] ; US Department of Energy [DE-SC0005248] ; US Department of Energy [DE-SC0005248] ; Southeastern Universities Research Association ; Southeastern Universities Research Association ; Southeastern Universities Research Association ; Southeastern Universities Research Association ; China-US Theory Institute for Physics with Exotic Nuclei [DESC0009971] ; China-US Theory Institute for Physics with Exotic Nuclei [DESC0009971] ; China-US Theory Institute for Physics with Exotic Nuclei [DESC0009971] ; China-US Theory Institute for Physics with Exotic Nuclei [DESC0009971] ; National Natural Science Foundation of China [11375080, 11675071] ; National Natural Science Foundation of China [11375080, 11675071] ; National Natural Science Foundation of China [11375080, 11675071] ; National Natural Science Foundation of China [11375080, 11675071] ; Australian Research Council Discovery Project [DP140101492] ; Australian Research Council Discovery Project [DP140101492] ; Australian Research Council Discovery Project [DP140101492] ; Australian Research Council Discovery Project [DP140101492] ; LSU-LNNU Joint Research Program [9961] ; LSU-LNNU Joint Research Program [9961] ; LSU-LNNU Joint Research Program [9961] ; LSU-LNNU Joint Research Program [9961] |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.itp.ac.cn/handle/311006/22140 |
Collection | 理论物理所科研产出_SCI论文 |
Corresponding Author | Zhang, YZ (reprint author), Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia.; Zhang, YZ (reprint author), Chinese Acad Sci, CAS Key Lab Theoret Phys, Inst Theoret Phys, Beijing 100190, Peoples R China. |
Recommended Citation GB/T 7714 | Pan, F,Zhang, YZ,Draayer, JP,et al. Exact solution of the two-axis countertwisting hamiltonian for the half-integer J case[J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,2017:23104. |
APA | Pan, F,Zhang, YZ,Draayer, JP,Zhang, YZ ,&Zhang, YZ .(2017).Exact solution of the two-axis countertwisting hamiltonian for the half-integer J case.JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,23104. |
MLA | Pan, F,et al."Exact solution of the two-axis countertwisting hamiltonian for the half-integer J case".JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2017):23104. |
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