Communications in Mathematical Physics最新文献

{"title":"Rigidity Results for Finite Energy Solutions to the Stationary 2D Euler Equations","authors":"Fabio De Regibus,&nbsp;Francesco Esposito,&nbsp;David Ruiz","doi":"10.1007/s00220-026-05660-y","DOIUrl":"10.1007/s00220-026-05660-y","url":null,"abstract":"<div><p>In this paper we prove rigidity results for classical solutions to the stationary 2D Euler equations in <span>(mathbb {R}^2)</span>. Assuming that the velocity field has finite energy and that the stagnation set is connected, we prove that the corresponding stream function solves an autonomous semilinear elliptic equation. Under some extra conditions on the vorticity near infinity we can also prove that the streamlines are concentric circles. The proofs include several energy estimates on the behavior of the stream function at infinity, as well as an adaptation of the continuous Steiner symmetrization to our setting.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 8","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-026-05660-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Optimal Convergence Rates in Trace Distance and Relative Entropy for the Quantum Central Limit Theorem","authors":"Salman Beigi,&nbsp;Milad M. Goodarzi,&nbsp;Hami Mehrabi","doi":"10.1007/s00220-026-05674-6","DOIUrl":"10.1007/s00220-026-05674-6","url":null,"abstract":"<div><p>A quantum analogue of the Central Limit Theorem (CLT) for bosonic system, first introduced by Cushen and Hudson (1971), states that the <i>n</i>-fold convolution <span>(rho ^{boxplus n})</span> of an <i>m</i>-mode quantum state <span>(rho )</span>—with zero first moments and finite second moments—converges weakly, as <i>n</i> increases, to a Gaussian state <span>(rho _G)</span> with the same first and second moments as those of <span>(rho )</span>, called its Gaussification. Recently, this result has been extended with estimates of the convergence rate in various distance measures. In this paper, we establish optimal rates of convergence in both the trace distance and quantum relative entropy. Specifically, we show that for a centered <i>m</i>-mode quantum state with finite third-order moments, the trace distance between <span>(rho ^{boxplus n})</span> and <span>(rho _G)</span> decays at the optimal rate of <span>(mathcal {O}(n^{-1/2}))</span>. Furthermore, for states with finite fourth-order moments (order <span>(4+delta )</span> for an arbitrary small <span>(delta &gt;0)</span> if <span>(m&gt;1)</span>), we prove that the relative entropy between <span>(rho ^{boxplus n})</span> and <span>(rho _G)</span> decays at the optimal rate of <span>(mathcal {O}(n^{-1}))</span>. Both of these rates are proven to be optimal, even when assuming the finiteness of all moments of <span>(rho )</span>. These results relax previous assumptions on higher-order moments, yielding convergence rates that match the best known results in the classical setting. By giving explicit examples we also show that our moment assumptions are essentially minimal. We show that for any <span>(theta &gt;0)</span>, there exists a quantum state <span>(rho )</span> with finite moments of order less than <span>(3-theta )</span>, such that the convergence rate of <span>(rho ^{boxplus n})</span> to <span>(rho _G)</span> in trace distance is not <span>(mathcal {O}(n^{-1/2}))</span>. Similarly, we show that for any <span>(theta &gt;0)</span>, there exists a quantum state <span>(rho )</span> with finite moments of order less than <span>(4-theta )</span>, such that the relative entropy between <span>(rho ^{boxplus n})</span> to <span>(rho _G)</span> does not decay at the rate <span>(mathcal {O}(n^{-1}))</span>. Our proofs draw on techniques from the classical literature, including Edgeworth-type expansions of quantum characteristic functions, adapted to the quantum context. A key technical step in the proof of our entropic CLT is establishing an upper bound on the relative entropy distance between a general quantum state and its Gaussification, which is of independent interest.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 8","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Mermin–Wagner Theorem for Dimers, Monomer Double-Dimers, and Spatial Random Permutations","authors":"Lorenzo Taggi,&nbsp;Wei Wu","doi":"10.1007/s00220-026-05626-0","DOIUrl":"10.1007/s00220-026-05626-0","url":null,"abstract":"<div><p>We study the double–dimer model, the monomer double–dimer model, spatial random permutations, and the dimer model. For this entire class of models, we prove absence of long-range order on two-dimensional graphs, both planar and non-planar. More precisely, long-range order is excluded in the sense of vanishing spontaneous magnetization; moreover, correlations and the probability that a loop visits two vertices decay to zero in an averaged sense as the distance between the vertices diverges. As a further consequence, we show that giant loops are absent, in sharp contrast with the behavior in dimensions <span>(d&gt;2)</span>. Our approach is based on the introduction of a new complex spin representation for all models in this class, together with a new proof of the Mermin–Wagner theorem that does not require positivity of the Gibbs measure. Even for the well-studied dimer and double-dimer models our results are new: since they do not rely on exact solvability or Kasteleyn’s theorem, they apply beyond the planar-graph setting.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 8","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Properly Outer Actions of Tensor Categories on C(^*)-Algebras","authors":"Roberto Hernández Palomares,&nbsp;Miho Mukohara","doi":"10.1007/s00220-026-05665-7","DOIUrl":"10.1007/s00220-026-05665-7","url":null,"abstract":"<div><p>We discuss proper outerness for finite-index endomorphisms and finite-index bimodules of simple C<span>(^*)</span>-algebras. The notion of properly outer automorphisms of von Neumann algebras was introduced by Connes, and the C<span>(^*)</span>-algebraic analogue for automorphisms has also been extensively investigated. Proper outerness is a strengthened form of outerness for automorphisms, endomorphisms, and bimodules of C<span>(^*)</span>-algebras, and may be viewed as a noncommutative analogue of topological freeness for homeomorphisms of locally compact spaces. It is a classical theorem of Kishimoto that every outer automorphism of a simple C<span>(^*)</span>-algebra is properly outer. As an application, he proved the simplicity of crossed product C<span>(^*)</span>-algebras arising from outer actions of discrete groups on simple C<span>(^*)</span>-algebras. More recently, Izumi proved that finite-index outer endomorphisms of purely infinite simple C<span>(^*)</span>-algebras are automatically properly outer. In this article, we extend Izumi’s result beyond the purely infinite setting. Our main result is that every finite-index outer endomorphism of a simple C<span>(^*)</span>-algebra is properly outer. Understanding finite-index endomorphisms is useful for studying symmetries beyond group actions, including actions by unitary tensor categories. As a consequence of our main result, freeness for outer actions of unitary tensor categories on simple C<span>(^*)</span>-algebras is also shown to hold automatically. As applications, we obtain structural results about irreducible discrete inclusions of C<span>(^*)</span>-algebras, potentially having infinite index, such as C<span>(^*)</span>-irreducibility in the sense of Rørdam.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 8","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Global Structure in the Presence of a Topological Defect","authors":"Arun Debray,&nbsp;Weicheng Ye,&nbsp;Matthew Yu","doi":"10.1007/s00220-026-05629-x","DOIUrl":"10.1007/s00220-026-05629-x","url":null,"abstract":"<div><p>We investigate the global structure of topological defects which wrap a submanifold <span>(Fsubset M)</span> in a quantum field theory defined on a closed manifold <i>M</i>. The Pontryagin–Thom construction oversees the interplay between the global structure of <i>F</i> and the global structure of <i>M</i>. We will employ this construction in two distinct mathematical frameworks with physical applications. The first framework is the concept of a characteristic structure, consisting of the data of pairs of manifolds (<i>M</i>, <i>F</i>) where <i>F</i> is Poincaré dual to some characteristic class. This concept is discussed in the mathematics literature and shown here to have meaningful physical interpretations related to defects. In our examples, we will mainly focus on the case where <i>M</i> is 4-dimensional and <i>F</i> has codimension 2. The second framework uses obstruction theory and the fact that spontaneously broken finite symmetries leave behind domain walls, to determine the conditions on which dimensions a higher-form finite symmetry can spontaneously break. We explicitly study the cases of higher-form <span>(mathbb {Z}/2)</span> symmetry, but the method can be generalized to other groups.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 8","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-026-05629-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of (alpha )-z Relative Entropies","authors":"Frits Verhagen,&nbsp;Marco Tomamichel,&nbsp;Erkka Haapasalo","doi":"10.1007/s00220-026-05675-5","DOIUrl":"10.1007/s00220-026-05675-5","url":null,"abstract":"<div><p>We offer the first operational interpretation of the <span>(alpha )</span>-<i>z</i> relative entropies, a measure of distinguishability between two quantum states introduced by Jakšić et al. and Audenaert and Datta. We show that these relative entropies appear when formulating conditions for large-sample or catalytic majorization of pairs of flat states and certain generalizations of them. Indeed, we show that such transformations exist if and only if all the <span>(alpha )</span>-<i>z</i> relative entropies for <span>(alpha &lt;1)</span> of the two pairs are ordered. In this setting, the <span>(alpha )</span> and <i>z</i> parameters are truly independent from each other. These results also yield an expression for the optimal rate of converting one flat state pair into another. Our methods use real-algebraic techniques involving preordered semirings and certain monotone homomorphisms and derivations on them.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 7","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Anomalies for Conformal Nets Associated with Lattices and T-Kernels","authors":"Marcel Bischoff,&nbsp;Pradyut Karmakar","doi":"10.1007/s00220-026-05723-0","DOIUrl":"10.1007/s00220-026-05723-0","url":null,"abstract":"<div><p>Let <span>(Lsubseteq mathbb {R}^{n})</span> an even lattice and <span>(T_{L}=mathbb {R}^{n}/L)</span> the associated torus. Associated with <i>L</i> we construct <span>(T_{L})</span>-kernel on a hyperfinite factor type <span>(mathcal {A}_{L})</span>, i.e. a monomorphism <span>(T_{L}rightarrow textsf{Out}(mathcal {A}_{L}))</span>, and compute Sutherland’s Sutherland, C.E.: Cohomology and extensions of von Neumann algebras. I. Publ. Res. Inst. Math. Sci. <b>16</b>(1), 105–133 (1980); Sutherland, C.E.: Cohomology and extensions of von Neumann algebras. II. Publ. Res. Inst. Math. Sci. <b>16</b>(1), 135–174 (1980) obstruction class in <span>(H^{3}_{textrm{Borel}}(T_{L},mathbb {T})cong H^{4}(BT_{L},mathbb {Z}))</span>, which is an invariant of the <span>(T_{L})</span>-kernel and an obstruction to the existence of a twisted crossed product by <span>(T_{L})</span>. As a Corollary, we obtain that for any <i>n</i>-torus <i>T</i> any class in <span>(H^{3}_{textrm{Borel}}(T,mathbb {T}))</span> arises as an obstruction for a <i>T</i>-kernel on the hyperfinite type III<span>(_{1})</span> factor <i>R</i>.</p><p>The construction is an analogue of the construction of Vaughan Jones for finite groups on the hyperfinite type II<span>(_{1})</span> factor but is also motivated by and has applications to conformal nets. Namely, there is an associated local extension <span>(mathcal {A}_{L}supseteq mathcal {A}_{mathbb {R}^n})</span> of conformal nets and the <span>(T_{L})</span>-kernel corresponds to a family of <span>(T_{L^*})</span>-twisted sectors representations whose anomaly (obstruction) can be identified with the inner product on <i>L</i> seen as a class in <span>(H^{4}(BT_{L},mathbb {Z})cong operatorname {Sym}^{2}(L,mathbb {Z}))</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 7","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"An Alexander-Like Theorem for a Particle Model with Inelastic Collisions","authors":"Théophile Dolmaire,&nbsp;Juan J. L. Velázquez","doi":"10.1007/s00220-026-05673-7","DOIUrl":"10.1007/s00220-026-05673-7","url":null,"abstract":"<div><p>We consider a finite system of hard spheres that collide inelastically according to a particular model, losing a fixed amount of kinetic energy at each collision. We develop the theory of the Transport-Collision-Transport (TCT) dynamics, which allows to study precisely the evolution of the Lebesgue measure in the phase space under the action of the flows of particle systems that can interact via instantaneous binary collision. In the two-dimensional case, we show that the scattering mapping associated to the inelastic hard sphere system that we introduce preserves locally the Lebesgue measure in the velocity space, in spite of the fact that a positive amount of kinetic energy is lost at each inelastic collision. We prove the analog of Alexander’s theorem for our model, which allows us to deduce the global well-posedness of the trajectories, for almost every initial datum, in dimension <i>d</i> arbitrary.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 7","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-026-05673-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"A Mathematical Analysis of IPT-DMFT","authors":"Eric Cancès,&nbsp;Alfred Kirsch,&nbsp;Solal Perrin-Roussel","doi":"10.1007/s00220-026-05647-9","DOIUrl":"10.1007/s00220-026-05647-9","url":null,"abstract":"<div><p>We provide a mathematical analysis of the Dynamical Mean-Field Theory (DMFT), a celebrated representative of a class of approximations in quantum mechanics known as <i>embedding methods</i>. Within the simplest setting of this approximation, which we introduce briefly at this point, we prove that, under certain assumptions, the DMFT equations admit a solution for any set of physical parameters. Moreover, we establish some properties of the solution(s). For the reader’s convenience, we provide in appendix a pedagogical and self-contained mathematical formulation of the DMFT equations for the finite Hubbard model. After recalling the definition and properties of one-body time-ordered Green’s functions and self-energies, and the mathematical structure of the Hubbard and Anderson impurity models, we describe the specific <i>impurity solver</i> we have studied in this article, namely the Iterated Perturbation Theory (IPT) solver, which can be conveniently formulated using Matsubara’s Green’s functions.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 7","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-026-05647-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Localization of Strings on Group Manifolds","authors":"Sameer Murthy,&nbsp;Edward Witten","doi":"10.1007/s00220-026-05663-9","DOIUrl":"10.1007/s00220-026-05663-9","url":null,"abstract":"<div><p>We compute the partition function of the WZW model with target a compact Lie group <i>G</i> by adapting a method used by Choi and Takhtajan to compute the heat kernel of the group manifold. The basic idea is to compute the partition function of a supersymmetric version of the WZW model using a form of supersymmetric localization and then use the fact that, since the fermions of the supersymmetric WZW model are actually decoupled from the bosons, this also determines the partition function of the purely bosonic WZW model. The result is a formula for the partition function as a sum over contributions from abelian classical solutions. We verify for <span>(G=SU(2))</span> that this formula agrees with the result for the same partition function that comes from the Weyl-Kac character formula. We extend the method of supersymmetric localization to certain related models such as the <span>(SL(2,{mathbb {R}}))</span> WZW model and a Wick-rotated version of this model in which the target space is hyperbolic three-space <span>(H_3^+)</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 7","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-026-05663-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}