{"title":"On light cone bounds for Markov quantum open systems","authors":"Israel Michael Sigal, Xiaoxu Wu","doi":"10.1007/s11005-026-02086-4","DOIUrl":"10.1007/s11005-026-02086-4","url":null,"abstract":"<div><p>We study space-time behaviour of solutions of the von Neumann–Lindblad equations underlying the dynamics of Markov quantum open systems. For a large class of these equations, we prove the existence of an effective light cone with an exponentially small spill-over.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147828577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the mean-field antiferromagnetic gap for the half-filled 2D Hubbard model at zero temperature","authors":"E. Langmann, J. Lenells","doi":"10.1007/s11005-026-02085-5","DOIUrl":"10.1007/s11005-026-02085-5","url":null,"abstract":"<div><p>We consider the antiferromagnetic gap for the half-filled two-dimensional (2D) Hubbard model (on a square lattice) at zero temperature in Hartree–Fock theory. It was conjectured by Hirsch in 1985 that this gap, <span>(Delta )</span>, vanishes like <span>(exp (-2pi sqrt{t/U}))</span> in the weak-coupling limit <span>(U/tdownarrow 0)</span> (<span>(U>0)</span> and <span>(t>0)</span> are the usual Hubbard model parameters). We give a proof of this conjecture based on recent mathematical results about Hartree-Fock theory for the 2D Hubbard model. The key step is the exact computation of an integral involving the density of states of the 2D tight binding band relation.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02085-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dispersionless version of multi-component Pfaff–Toda hierarchy","authors":"A. Savchenko, A. Zabrodin","doi":"10.1007/s11005-026-02084-6","DOIUrl":"10.1007/s11005-026-02084-6","url":null,"abstract":"<div><p>We consider the dispersionless limit of the recently introduced multi-component Pfaff–Toda hierarchy. Its dispersionless version is a set of nonlinear differential equations for the dispersionless limit of logarithm of the tau-function (the <i>F</i>-function). They are obtained as limiting cases of bilinear equations of the Hirota–Miwa type. The analysis of the Pfaff–Toda hierarchy is substantially simplified by using the observation that the full (not only dispersionless) <i>N</i>-component Pfaff–Toda hierarchy is actually equivalent to the 2<i>N</i>-component DKP hierarchy. In the dispersionless limit, there is an elliptic curve built in the structure of the hierarchy, with the elliptic modular parameter being a dynamical variable. This curve can be uniformized by elliptic functions, and in the elliptic parametrization the hierarchy acquires a compact and especially nice form.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantum error correction in Kitaev’s quantum double model for Abelian groups","authors":"Shawn X. Cui, César Galindo, Diego Romero","doi":"10.1007/s11005-026-02076-6","DOIUrl":"10.1007/s11005-026-02076-6","url":null,"abstract":"<div><p>In this paper, we present a detailed mathematical description of the error correction process for Kitaev’s model for finite Abelian groups. The number of errors Kitaev’s model can correct depends on the lattice and its topology. Although there is a theoretical maximum number of errors that can be corrected, we prove that correcting this number of errors, in general, is an NP-complete problem. Consequently, we introduce a polynomial-time correction algorithm that corrects a number of errors below the theoretical maximum.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linear coactions of discrete quantum groups on the circle","authors":"Debashish Goswami, Suchetana Samadder","doi":"10.1007/s11005-026-02083-7","DOIUrl":"10.1007/s11005-026-02083-7","url":null,"abstract":"<div><p>For a (unital) <span>(C^*)</span>-algebra <span>(mathcal{A})</span>, we construct a <span>(C^*)</span>-algebraic discrete quantum group (DQG) <span>(mathcal{Q}_textrm{aut}(mathcal{A}))</span>, coacting on <span>(mathcal{A})</span>, which is a quantum generalization of <span>({text{ A }ut}(mathcal{A}))</span> in the framework of discrete quantum groups, in the sense that any other coaction of a DQG on <span>(mathcal{A})</span> factors through the above coaction of <span>(mathcal{Q}_textrm{aut}(mathcal{A}))</span>. We prove by an explicit calculation that if any Kac-type <span>(C^*)</span>-algebraic discrete quantum group <span>(mathcal {Q})</span> has a ‘weakly faithful’ coaction on <span>(C(S^1))</span> which is ‘linear’ in the sense that it leaves the space spanned by <span>({ Z, overline{Z} })</span> invariant, then <span>(mathcal {Q})</span> must be classical i.e. isomorphic with <span>(C_0(Gamma ))</span> for some discrete group <span>(Gamma )</span>. This parallels the well-known result of non-existence of genuine compact quantum group symmetry obtained by the first author and his collaborators Goswami (Quantum isometry groups, Infosys Science Foundation Series, Springer, Cham, 2016) and the references therein).\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Elliptic solutions of the lattice CKP equation and its elliptic direct linearisation scheme","authors":"Ying-ying Sun, Da-jun Zhang, Frank Nijhoff","doi":"10.1007/s11005-026-02077-5","DOIUrl":"10.1007/s11005-026-02077-5","url":null,"abstract":"<div><p>A direct linearisation scheme, based on an elliptic Cauchy kernel, is set up for the lattice CKP equation. This leads to an elliptic parametrisation of the lattice CKP equation, which allows us to perform appropriate continuum limits and construct elliptic solutions. By selecting appropriate integration measures and domains for the singular linear integral equation in the scheme, elliptic multi-soliton solutions of the lattice CKP equation are found. Also a Lax triplet associated with the system is derived from the direct linearisation scheme.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A note on measures whose diffraction is concentrated on a single sphere","authors":"Michael Baake, Emily R. Korfanty, Jan Mazáč","doi":"10.1007/s11005-026-02081-9","DOIUrl":"10.1007/s11005-026-02081-9","url":null,"abstract":"<div><p>Is there a translation-bounded measure whose diffraction is spherically symmetric and concentrated on a single sphere? This note constructively answers this question of Strungaru in the affirmative.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02081-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Metric convergence of sequences of static spacetimes with the null distance","authors":"Brian Allen","doi":"10.1007/s11005-026-02079-3","DOIUrl":"10.1007/s11005-026-02079-3","url":null,"abstract":"<div><p>How should one define metric space notions of convergence for sequences of spacetimes? Since a Lorentzian manifold does not define a metric space directly, the uniform convergence, Gromov-Hausdorff (GH) convergence, and Sormani-Wenger Intrinsic Flat (SWIF) convergence does not extend automatically. One approach is to define a metric space structure, which is compatible with the Lorentzian structure, so that the usual notions of convergence apply. This approach was taken by C. Sormani and C. Vega [Sormani, C., Vega, C.: Null distance on a spacetime, Classical Quantum Gravity 33, no. 8, 085001, 29. (2016) MR3476515] when defining the null distance. In this paper, we study sequences of static spacetimes equipped with the null distance under uniform, GH, and SWIF convergence, as well as Hölder bounds. We use the results of the Volume Above Distance Below (VADB) theorem of the author, R. Perales, and C. Sormani [Allen, B., Perales, R., Sormani, C.: Volume above distance below. J. Differential Geom. <b>126</b>(3), 837–874 (2024)] to prove an analog of the VADB theorem for sequences of static spacetimes with the null distance. We also give a conjecture of what the VADB theorem should be in the case of sequences of globally hyperbolic spacetimes with the null distance.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Classification of uniformly bounded simple Lie conformal algebras with upper bound one","authors":"Maosen Xu, Huangjie Yu, Lipeng Luo","doi":"10.1007/s11005-026-02078-4","DOIUrl":"10.1007/s11005-026-02078-4","url":null,"abstract":"<div><p>In this paper, we prove that uniformly bounded simple Lie conformal algebras must be finitely generated as algebras. Furthermore, we give a complete classification of uniformly bounded simple Lie conformal algebras with upper bound one.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147606412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The 4-fold Pandharipande–Thomas vertex and Jeffrey–Kirwan residue","authors":"Taro Kimura, Go Noshita","doi":"10.1007/s11005-026-02071-x","DOIUrl":"10.1007/s11005-026-02071-x","url":null,"abstract":"<div><p>We present a contour integral formalism for computing the K-theoretic equivariant Pandharipande–Thomas (PT) 4-vertex. Within the Jeffrey–Kirwan (JK) residue framework, we show that the PT 4-vertex can be obtained from the same integrand as the Donaldson–Thomas (DT) 4-vertex by choosing a different reference vector. We illustrate the formalism through examples involving curves and surfaces on the 4-fold. Furthermore, we investigate the DT/PT correspondence for the 4-fold setting together with its higher rank and supergroup-like generalizations.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147606448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}