Shannon entropy of optimized proton-neutron pair condensates
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929587528663040 |
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| author | Liang, Shu-Yuan Lu, Yi Lei, Yang Johnson, Calvin W. Fu, Guan-Jian Shen, Jia Jie |
| author_facet | Liang, Shu-Yuan Lu, Yi Lei, Yang Johnson, Calvin W. Fu, Guan-Jian Shen, Jia Jie |
| contents | Proton-neutron pairing and like-nucleon pairing are two different facets of atomic nuclear configurations. While like-nucleon pair condensates manifest their superfluidic nature in semi magic nuclei, it is not absolutely clear if there exists a T=0 proton-neutron pair condensate phase in $N=Z$ nuclei. With an explicit formalism of general pair condensates with good particle numbers, we optimize proton-neutron pair condensates for all $N=Z$ nuclei between $^{16}$O and $^{100}$Sn, given shell model effective interactions. As comparison, we also optimize like-nucleon pair condensates for their semi-magic isotones. Shannon entanglement entropy is a measurement of mixing among pair configurations, and can signal intrinsic phase transition. It turns out the like-nucleon pair condensates for semi-magic nuclei have large entropies signaling an entangled phase, but the proton-neutron pair condensates end up not far from a Hartree-Fock solution, with small entropy. With artificial pairing interaction strengths, we show that the general proton-neutron pair condensate can transit from an entangled T=1 phase to an entangled T=0 phase, i.e. pairing phase transition driven by external parameters. In the T=0 limit, the proton-neutron pair condensate optimized for $^{24}$Mg turns out to be a purely P pair condensate with large entanglement entropy, although such cases may occur in cold atom systems, unlikely in atomic nuclei. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01439 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shannon entropy of optimized proton-neutron pair condensates Liang, Shu-Yuan Lu, Yi Lei, Yang Johnson, Calvin W. Fu, Guan-Jian Shen, Jia Jie Nuclear Theory Proton-neutron pairing and like-nucleon pairing are two different facets of atomic nuclear configurations. While like-nucleon pair condensates manifest their superfluidic nature in semi magic nuclei, it is not absolutely clear if there exists a T=0 proton-neutron pair condensate phase in $N=Z$ nuclei. With an explicit formalism of general pair condensates with good particle numbers, we optimize proton-neutron pair condensates for all $N=Z$ nuclei between $^{16}$O and $^{100}$Sn, given shell model effective interactions. As comparison, we also optimize like-nucleon pair condensates for their semi-magic isotones. Shannon entanglement entropy is a measurement of mixing among pair configurations, and can signal intrinsic phase transition. It turns out the like-nucleon pair condensates for semi-magic nuclei have large entropies signaling an entangled phase, but the proton-neutron pair condensates end up not far from a Hartree-Fock solution, with small entropy. With artificial pairing interaction strengths, we show that the general proton-neutron pair condensate can transit from an entangled T=1 phase to an entangled T=0 phase, i.e. pairing phase transition driven by external parameters. In the T=0 limit, the proton-neutron pair condensate optimized for $^{24}$Mg turns out to be a purely P pair condensate with large entanglement entropy, although such cases may occur in cold atom systems, unlikely in atomic nuclei. |
| title | Shannon entropy of optimized proton-neutron pair condensates |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2411.01439 |