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On Bose–Einstein condensates in the Thomas–Fermi regime 论托马斯-费米体系中的玻色-爱因斯坦凝聚体
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-10-14 DOI: 10.1007/s11040-022-09439-0
Daniele Dimonte, Emanuela L. Giacomelli
{"title":"On Bose–Einstein condensates in the Thomas–Fermi regime","authors":"Daniele Dimonte,&nbsp;Emanuela L. Giacomelli","doi":"10.1007/s11040-022-09439-0","DOIUrl":"10.1007/s11040-022-09439-0","url":null,"abstract":"<div><p>We study a system of <i>N</i> trapped bosons in the Thomas–Fermi regime with an interacting pair potential of the form <span>( g_N N^{3beta -1} V(N^beta x) )</span>, for some <span>( beta in (0,1/3) )</span> and <span>( g_N )</span> diverging as <span>( N rightarrow infty )</span>. We prove that there is complete Bose–Einstein condensation at the level of the ground state and, furthermore, that, if <span>( beta in (0,1/6) )</span>, condensation is preserved by the time evolution.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09439-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4882957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Limit Theorems for Multi-group Curie–Weiss Models via the Method of Moments 基于矩量法的多群Curie-Weiss模型极限定理
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-09-24 DOI: 10.1007/s11040-022-09433-6
Werner Kirsch, Gabor Toth
{"title":"Limit Theorems for Multi-group Curie–Weiss Models via the Method of Moments","authors":"Werner Kirsch,&nbsp;Gabor Toth","doi":"10.1007/s11040-022-09433-6","DOIUrl":"10.1007/s11040-022-09433-6","url":null,"abstract":"<div><p>We study a multi-group version of the mean-field or Curie–Weiss spin model. For this model, we show how, analogously to the classical (single-group) model, the three temperature regimes are defined. Then we use the method of moments to determine for each regime how the vector of the group magnetisations behaves asymptotically. Some possible applications to social or political sciences are discussed.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09433-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4954524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Conjugate Frobenius Manifold and Inversion Symmetry 共轭Frobenius流形与反演对称性
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-09-12 DOI: 10.1007/s11040-022-09436-3
Zainab Al-Maamari, Yassir Dinar
{"title":"Conjugate Frobenius Manifold and Inversion Symmetry","authors":"Zainab Al-Maamari,&nbsp;Yassir Dinar","doi":"10.1007/s11040-022-09436-3","DOIUrl":"10.1007/s11040-022-09436-3","url":null,"abstract":"<div><p>We give a conjugacy relation on certain type of Frobenius manifold structures using the theory of flat pencils of metrics. It leads to a geometric interpretation for the inversion symmetry of solutions to Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48415836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Frobenius Manifolds on Orbits Spaces 轨道空间上的Frobenius歧管
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-08-25 DOI: 10.1007/s11040-022-09434-5
Zainab Al-Maamari, Yassir Dinar
{"title":"Frobenius Manifolds on Orbits Spaces","authors":"Zainab Al-Maamari,&nbsp;Yassir Dinar","doi":"10.1007/s11040-022-09434-5","DOIUrl":"10.1007/s11040-022-09434-5","url":null,"abstract":"<div><p>The orbits space of an irreducible linear representation of a finite group is a variety whose coordinate ring is the ring of invariant polynomials. Boris Dubrovin proved that the orbits space of the standard reflection representation of an irreducible finite Coxeter group <span>({mathcal {W}})</span> acquires a natural polynomial Frobenius manifold structure. We apply Dubrovin’s method on various orbits spaces of linear representations of finite groups. We find some of them has non or several natural Frobenius manifold structures. On the other hand, these Frobenius manifold structures include rational and trivial structures which are not known to be related to the invariant theory of finite groups.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09434-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43518701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Equivariant Spectral Triples for Homogeneous Spaces of the Compact Quantum Group (U_q(2)) 紧量子群齐次空间的等变谱三元组 (U_q(2))
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-08-08 DOI: 10.1007/s11040-022-09432-7
Satyajit Guin, Bipul Saurabh
{"title":"Equivariant Spectral Triples for Homogeneous Spaces of the Compact Quantum Group (U_q(2))","authors":"Satyajit Guin,&nbsp;Bipul Saurabh","doi":"10.1007/s11040-022-09432-7","DOIUrl":"10.1007/s11040-022-09432-7","url":null,"abstract":"<div><p>In this article, we study homogeneous spaces <span>(U_q(2)/_phi mathbb {T})</span> and <span>(U_q(2)/_psi mathbb {T})</span> of the compact quantum group <span>(U_q(2),,qin {mathbb {C}}setminus {0})</span>. The homogeneous space <span>(U_q(2)/_phi mathbb {T})</span> is shown to be the braided quantum group <span>(SU_q(2))</span>. The homogeneous space <span>(U_q(2)/_psi mathbb {T})</span> is established as a universal <span>(C^*)</span>-algebra given by a finite set of generators and relations. Its <span>({mathcal {K}})</span>-groups are computed and two families of finitely summable odd spectral triples, one is <span>(U_q(2))</span>-equivariant and the other is <span>(mathbb {T}^2)</span>-equivariant, are constructed. Using the index pairing, it is shown that the induced Fredholm modules for these families of spectral triples give each element in the <span>({mathcal {K}})</span>-homology group <span>(K^1(C(U_q(2)/_psi mathbb {T})))</span>.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Gauge Symmetries and Renormalization 规范对称性与重整化
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-08-06 DOI: 10.1007/s11040-022-09423-8
David Prinz
{"title":"Gauge Symmetries and Renormalization","authors":"David Prinz","doi":"10.1007/s11040-022-09423-8","DOIUrl":"10.1007/s11040-022-09423-8","url":null,"abstract":"<div><p>We study the perturbative renormalization of quantum gauge theories in the Hopf algebra setup of Connes and Kreimer. It was shown by van Suijlekom (Commun Math Phys 276:773–798, 2007) that the quantum counterparts of gauge symmetries—the so-called Ward–Takahashi and Slavnov–Taylor identities—correspond to Hopf ideals in the respective renormalization Hopf algebra. We generalize this correspondence to super- and non-renormalizable Quantum Field Theories, extend it to theories with multiple coupling constants and add a discussion on transversality. In particular, this allows us to apply our results to (effective) Quantum General Relativity, possibly coupled to matter from the Standard Model, as was suggested by Kreimer (Ann Phys 323:49–60, 2008). To this end, we introduce different gradings on the renormalization Hopf algebra and study combinatorial properties of the superficial degree of divergence. Then we generalize known coproduct and antipode identities to the super- and non-renormalizable cases and to theories with multiple vertex residues. Building upon our main result, we provide criteria for the compatibility of these Hopf ideals with the corresponding renormalized Feynman rules. A direct consequence of our findings is the well-definedness of the Corolla polynomial for Quantum Yang–Mills theory without reference to a particular renormalization scheme.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09423-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49009761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Lattice Gauge Theory and a Random-Medium Ising Model 晶格规范理论与随机介质Ising模型
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-07-06 DOI: 10.1007/s11040-022-09430-9
Mikhail Skopenkov
{"title":"Lattice Gauge Theory and a Random-Medium Ising Model","authors":"Mikhail Skopenkov","doi":"10.1007/s11040-022-09430-9","DOIUrl":"10.1007/s11040-022-09430-9","url":null,"abstract":"<div><p>We study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09430-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4257427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Levi–Civita Connections on Quantum Spheres 量子球上的列维-西维塔联系
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-07-06 DOI: 10.1007/s11040-022-09431-8
Joakim Arnlind, Kwalombota Ilwale, Giovanni Landi
{"title":"Levi–Civita Connections on Quantum Spheres","authors":"Joakim Arnlind,&nbsp;Kwalombota Ilwale,&nbsp;Giovanni Landi","doi":"10.1007/s11040-022-09431-8","DOIUrl":"10.1007/s11040-022-09431-8","url":null,"abstract":"<div><p>We introduce <i>q</i>-deformed connections on the quantum 2-sphere and 3-sphere, satisfying a twisted Leibniz rule in analogy with <i>q</i>-deformed derivations. We show that such connections always exist on projective modules. Furthermore, a condition for metric compatibility is introduced, and an explicit formula is given, parametrizing all metric connections on a free module. On the quantum 3-sphere, a <i>q</i>-deformed torsion freeness condition is introduced and we derive explicit expressions for the Christoffel symbols of a Levi–Civita connection for a general class of metrics. We also give metric connections on a class of projective modules over the quantum 2-sphere. Finally, we outline a generalization to any Hopf algebra with a (left) covariant calculus and associated quantum tangent space.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09431-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4255091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Prolongations of Convenient Lie Algebroids 便利李代数群的延拓
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-06-21 DOI: 10.1007/s11040-022-09429-2
Patrick Cabau, Fernand Pelletier
{"title":"Prolongations of Convenient Lie Algebroids","authors":"Patrick Cabau,&nbsp;Fernand Pelletier","doi":"10.1007/s11040-022-09429-2","DOIUrl":"10.1007/s11040-022-09429-2","url":null,"abstract":"<div><p>We first define the concept of Lie algebroid in the convenient setting. In reference to the finite dimensional context, we adapt the notion of prolongation of a Lie algebroid over a fibred manifold to a convenient Lie algebroid over a fibred manifold. Then we show that this construction is stable under projective and direct limits under adequate assumptions.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4828523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Zeros of the Partition Function of the Pinning Model 钉钉模型配分函数的零点
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-06-09 DOI: 10.1007/s11040-022-09428-3
Giambattista Giacomin, Rafael L. Greenblatt
{"title":"The Zeros of the Partition Function of the Pinning Model","authors":"Giambattista Giacomin,&nbsp;Rafael L. Greenblatt","doi":"10.1007/s11040-022-09428-3","DOIUrl":"10.1007/s11040-022-09428-3","url":null,"abstract":"<div><p>We aim at understanding for which (complex) values of the potential the pinning partition function vanishes. The pinning model is a Gibbs measure based on discrete renewal processes with power law inter-arrival distributions. We obtain some results for rather general inter-arrival laws, but we achieve a substantially more complete understanding for a specific one parameter family of inter-arrivals. We show, for such a specific family, that the zeros asymptotically lie on (and densely fill) a closed curve that, unsurprisingly, touches the real axis only in one point (the critical point of the model). We also perform a sharper analysis of the zeros close to the critical point and we exploit this analysis to approach the challenging problem of Griffiths singularities for the disordered pinning model. The techniques we exploit are both probabilistic and analytical. Regarding the first, a central role is played by limit theorems for heavy tail random variables. As for the second, potential theory and singularity analysis of generating functions, along with their interplay, will be at the heart of several of our arguments.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52479927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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