轻推松紧带和轻绑Skyrmions

IF 0.9 3区 物理与天体物理 Q2 MATHEMATICS
James Martin Speight, Thomas Winyard
{"title":"轻推松紧带和轻绑Skyrmions","authors":"James Martin Speight, Thomas Winyard","doi":"10.3842/sigma.2023.073","DOIUrl":null,"url":null,"abstract":"It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) $B$. Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given $B$) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for $5\\leq B\\leq 10$. We go on to complete the quantization for $B=7$, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin $1/2$ do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"198 1","pages":"0"},"PeriodicalIF":0.9000,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Nudged Elastic Bands and Lightly Bound Skyrmions\",\"authors\":\"James Martin Speight, Thomas Winyard\",\"doi\":\"10.3842/sigma.2023.073\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) $B$. Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given $B$) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for $5\\\\leq B\\\\leq 10$. We go on to complete the quantization for $B=7$, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin $1/2$ do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.\",\"PeriodicalId\":49453,\"journal\":{\"name\":\"Symmetry Integrability and Geometry-Methods and Applications\",\"volume\":\"198 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-10-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symmetry Integrability and Geometry-Methods and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3842/sigma.2023.073\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry Integrability and Geometry-Methods and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3842/sigma.2023.073","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1

摘要

近年来已经清楚地表明,核Skyrme模型的构型空间在每个拓扑类中都有许多几乎简并的局部能量极小值,并且这种极小值的数量随着程度(或重子数)$B$的增加而增加。在刚体量子化中,人们量子化在一个最小值的自旋-同位旋轨道上的运动,因此是一个不合理的近似。相反,我们应该确定一个(有限维)模空间,它包含所有的局部极小值(对于给定的$B$)以及它们之间平滑插值的域。本文提出了生成这样一个模空间的系统计算方案:在每一对局部极小值之间构造能量最小路径,然后将模空间定义为这些曲线并集上点的自旋-同位旋轨道的并集,即图上的一个主束。在实际应用中,可以使用轻推弹性带法(一种分析反应路径和计算活化能的标准数学化学工具)来构造能量最小化曲线。为了说明这一点,我们将该方案应用于点粒子近似中的轻绑定Skyrme模型,构建$5\leq B\leq 10$的图。我们继续完成$B=7$的量化,其中图有两个顶点和一条边。具有同位旋$1/2$的低能级量子态不强烈地局域于任何一个局域能量最小值(顶点)附近。它们的能量随自旋单调上升,这与锂-7的实验数据相矛盾。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nudged Elastic Bands and Lightly Bound Skyrmions
It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) $B$. Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given $B$) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for $5\leq B\leq 10$. We go on to complete the quantization for $B=7$, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin $1/2$ do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
1.80
自引率
0.00%
发文量
87
审稿时长
4-8 weeks
期刊介绍: Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信