Communications in Mathematical Physics最新文献

{"title":"Restriction of Schrödinger Eigenfunctions to Submanifolds","authors":"Xiaoqi Huang,&nbsp;Xing Wang,&nbsp;Cheng Zhang","doi":"10.1007/s00220-026-05576-7","DOIUrl":"10.1007/s00220-026-05576-7","url":null,"abstract":"<div><p>For Schrödinger operators <span>(H_V=-Delta _g+V)</span> with critically singular potentials <i>V</i> on compact manifolds, we prove sharp estimates for the restriction of eigenfunctions to submanifolds. Our method refines the perturbative argument by Blair et al. (J Geom Anal 31(7):6624–6661, 2021) and enables us to deal with submanifolds of all codimensions. As applications, we obtain improved estimates on negatively curved manifolds and flat tori. In particular, we extend the uniform <span>(L^2)</span> restriction estimates on flat tori by Bourgain and Rudnick (Geom Funct Anal 22(4):878–937, 2012) to singular potentials.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147375244","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":"Gauss-Manin Connection in Disguise: Open Gromov-Witten Invariants","authors":"Felipe Espreafico","doi":"10.1007/s00220-025-05504-1","DOIUrl":"10.1007/s00220-025-05504-1","url":null,"abstract":"<div><p>In mirror symmetry, after the work by J. Walcher, the number of holomorphic disks with boundary on the real quintic lagrangian in a general quintic threefold is related to the periods of the mirror quintic family with boundary on two homologous rational curves, known as Deligne conics. Following the ideas of H. Movasati, we construct a quasi-affine space parametrizing such objects enhanced with a frame for the relative de Rham cohomology with boundary at the curves compatible with the mixed Hodge structure. We also compute a modular vector field attached to such a parametrization.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341295","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":"New Representations for the Virasoro Superalgebras","authors":"Xiangqian Guo,&nbsp;Shujuan Li,&nbsp;Xuewen Liu","doi":"10.1007/s00220-026-05562-z","DOIUrl":"10.1007/s00220-026-05562-z","url":null,"abstract":"<div><p>For any complex number <i>b</i> and nonzero complex number <span>(lambda )</span>, we construct a class of <span>(N=1)</span> Neveu-Schwarz algebra modules <span>(mathcal {L}(P,V,lambda ,b))</span> from module <i>P</i> over the Weyl superalgebra and restricted module <i>V</i> over the positive-part subalgebra of the <span>(N=1)</span> Neveu-Schwarz algebra. The necessary and sufficient conditions for <span>(mathcal {L}(P,V,lambda ,b))</span> to be irreducible are obtained. If such a module <span>(mathcal {L}(P,V,lambda ,b))</span> is not irreducible, we also construct its submodules concretely. Then we determine the necessary and sufficient conditions for two such Neveu-Schwarz Virasoro superalgebra modules to be isomorphic.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341435","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":"Universality in the Small-Dispersion Limit of the Benjamin–Ono Equation","authors":"Elliot Blackstone,&nbsp;Peter D. Miller,&nbsp;Matthew D. Mitchell","doi":"10.1007/s00220-025-05506-z","DOIUrl":"10.1007/s00220-025-05506-z","url":null,"abstract":"<div><p>We examine the solution of the Benjamin–Ono Cauchy problem for rational initial data in three types of double-scaling limits in which the dispersion tends to zero while simultaneously the independent variables either approach a point on one of the two branches of the caustic curve of the inviscid Burgers equation, or approach the critical point where the branches meet. The results reveal universal limiting profiles in each case that are independent of details of the initial data. We compare the results obtained with corresponding results for the Korteweg-de Vries equation found by Claeys–Grava in three papers (Claeys and Grava in Commun Math Phys 286:979–1009, 2009, Commun Pure Appl Math 63:203–232, 2010, SIAM J Math Anal 42:2132–2154, 2010). Our method is to analyze contour integrals appearing in an explicit representation of the solution of the Cauchy problem, in various limits involving coalescing saddle points.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05506-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341436","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":"The Scaling Limit of the Volume of Loop–O(n) Quadrangulations","authors":"Élie Aïdékon,&nbsp;William Da Silva,&nbsp;Xingjian Hu","doi":"10.1007/s00220-025-05527-8","DOIUrl":"10.1007/s00220-025-05527-8","url":null,"abstract":"<div><p>We study the volume of rigid loop–<i>O</i>(<i>n</i>) quadrangulations with a boundary of length 2<i>p</i> in the non-generic critical regime, for all <span>(nin (0,2])</span>. We prove that, as the half-perimeter <i>p</i> goes to infinity, the volume scales in distribution to an explicit random variable. This limiting random variable is described in terms of the multiplicative cascades of Chen et al. (Ann Inst Henri Poincaré D 7(4):535–584, 2020), or alternatively (in the dilute case) as the law of the area of a unit-boundary <span>(gamma )</span>–quantum disc, as determined by Ang and Gwynne (Ann Inst Henri Poincaré D 57(1): 1–53, 2021), for suitable <span>(gamma )</span>. Our arguments go through a classification of the map into several regions, where we rule out the contribution of bad regions to be left with a tractable portion of the map. One key observable for this classification is a Markov chain which explores the nested loops around a size-biased vertex pick in the map, making explicit the spinal structure of the discrete multiplicative cascade. We stress that our techniques enable us to include the boundary case <span>(n=2)</span>, that we define rigorously, and where the nested cascade structure is that of a critical branching random walk. In that case the scaling limit is given by the limit of the derivative martingale and is inverse-exponentially distributed, which answers a conjecture of Aïdékon and Da Silva (Probab Theory Relat Fields 183(1):125–166, 2022).</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12876490/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146140732","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":"Rare Events Statistics for (mathbb {Z}^d) Map Lattices Coupled by Collision","authors":"Wael Bahsoun,&nbsp;Maxence Phalempin","doi":"10.1007/s00220-026-05557-w","DOIUrl":"10.1007/s00220-026-05557-w","url":null,"abstract":"<div><p>Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate <span>(mathbb {Z}^d)</span>-map lattices coupled by collision with simplified local dynamics that offer significant insights for the above challenging problem. We obtain a first order approximation for the first collision rate at a site <span>({textbf{p}}^*in mathbb {Z}^d)</span> and we prove a distributional convergence for the first collision time to an exponential, with sharp error term. Moreover, we prove that the number of collisions at site <span>({textbf{p}}^*)</span> converge in distribution to a compound Poisson distributed random variable. Key to our analysis in this infinite dimensional setting is the use of transfer operators associated with the <i>decoupled</i> map lattice at site <span>({textbf{p}}^*)</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12876473/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146140687","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":"On Cauchy Problem for the Spin-1 Gross–Pitaevskii Equation: Soliton Resolution Conjecture and Asymptotic Analysis","authors":"Shou-Fu Tian,&nbsp;Jia-Fu Tong","doi":"10.1007/s00220-025-05551-8","DOIUrl":"10.1007/s00220-025-05551-8","url":null,"abstract":"<div><p>We investigate the Cauchy problem for the spin-1 Gross–Pitaevskii (GP) equation, which is a model instrumental in characterizing the soliton dynamics within spinor Bose-Einstein condensates. Recently, Geng et al. (Commun Math Phys 382:585–611, 2021) reported the long-time asymptotic result with error <span>(mathcal {O}(frac{ln t}{t}))</span> for the spin-1 GP equation for the case of the purely continuous spectrum. Based on the previous work, we conduct in-depth research on the soliton resolution conjecture and asymptotic analysis of the spin-1 GP equation. Compared with the previous work, we improve the asymptotic error accuracy from <span>(mathcal {O}(frac{ln t}{t}))</span> to <span>(mathcal {O}(t^{-3/4}))</span>. More importantly, through the <span>(bar{partial })</span>-nonlinear steepest descent method and the Deift–Zhou’s nonlinear steepest descent method, we obtain effective asymptotic errors and successfully carry out a full asymptotic analysis of the spin-1 GP equation based on the characteristics of the spectral problem, including three cases: (i) coexistence of discrete and continuous spectrum; (ii) the purely continuous spectrum, as considered in the work of Geng et al. with error <span>(mathcal {O}(frac{ln t}{t}))</span>; (iii) the purely discrete spectrum. For the case (i), the corresponding asymptotic approximations can be characterized by an <i>N</i>-solitons as well as an interaction term between soliton solutions and the dispersion term with diverse residual error order <span>(mathcal {O}(t^{-3/4}))</span>. In the case (ii), we strictly prove that the solution of the spin-1 GP equation can be characterized by the soliton solution and an error term with <span>(mathcal {O}(t^{-3/4}))</span>. For the case (iii), we rigorously prove the localization of multiple degenerate soliton groups (DSGs), which is comprised of inseparable solitons with identical velocities, and calculate the long-time asymptotics for an arbitrary <i>N</i>-soliton solutions of the spin-1 GP equation. Finally, our results confirm the soliton resolution conjecture of the spin-1 GP equation and show that the soliton solutions of the spin-1 GP equation become a linear combination of multiple DSGs with different sizes.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337279","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":"Hydrodynamic Limit for an Open Facilitated Exclusion Process with Slow and Fast Boundaries","authors":"Hugo Da Cunha,&nbsp;Clément Erignoux,&nbsp;Marielle Simon","doi":"10.1007/s00220-025-05550-9","DOIUrl":"10.1007/s00220-025-05550-9","url":null,"abstract":"<div><p>We study the symmetric <i>facilitated exclusion process</i> (FEP) on the finite one-dimensional lattice <span>(lbrace 1,hdots , N-1rbrace )</span> when put in contact with boundary reservoirs, whose action is subject to an additional kinetic constraint in order to enforce ergodicity, and whose speed is of order <span>(N^{-theta })</span> for some parameter <span>(theta )</span>. We derive its hydrodynamic limit as <span>(Nrightarrow infty )</span>, in the diffusive space-time scaling, when the initial density profile is supercritical. More precisely, the macroscopic density of particles evolves in the bulk according to a fast diffusion equation as in the periodic case, which is now subject to boundary conditions that can be of Dirichlet, Robin or Neumann type depending on the parameter <span>(theta )</span>. In the Dirichlet case, the FEP exhibits a very peculiar behaviour: unlike for the classical SSEP, and due to the two-phased nature of FEP, the reservoirs impose boundary densities which do not coincide with their equilibrium densities. The proof is based on the classical entropy method, but requires significant adaptations to account for the FEP’s non-product stationary states and to deal with the non-equilibrium setting.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337180","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":"Einstein Metrics on Homogeneous Superspaces","authors":"Yang Zhang,&nbsp;Mark D. Gould,&nbsp;Artem Pulemotov,&nbsp;Jørgen Rasmussen","doi":"10.1007/s00220-025-05539-4","DOIUrl":"10.1007/s00220-025-05539-4","url":null,"abstract":"<div><p>This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a construction of homogeneous supermanifolds by means of Dynkin diagrams, resembling the construction of generalised flag manifolds in classical (non-super) theory. We describe the Einstein metrics on several classes of spaces obtained through this approach. Our results provide examples of compact homogeneous supermanifolds on which the Einstein equation has no solutions, discrete families of solutions, and continuous families of Ricci-flat solutions among invariant metrics. These examples demonstrate that the finiteness conjecture from classical homogeneous geometry fails on supermanifolds, and challenge the intuition furnished by Bochner’s vanishing theorem.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05539-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337185","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":"Cubic Dirac Operators and Dirac Cohomology for Basic Classical Lie Superalgebras","authors":"Simone Noja,&nbsp;Steffen Schmidt,&nbsp;Raphael Senghaas","doi":"10.1007/s00220-025-05547-4","DOIUrl":"10.1007/s00220-025-05547-4","url":null,"abstract":"<div><p>We study the Dirac cohomology of supermodules over basic classical Lie superalgebras, formulated in terms of cubic Dirac operators associated with parabolic subalgebras. Specifically, we establish a super-analog of the Casselman–Osborne theorem for supermodules with an infinitesimal character and use it to show that the Dirac cohomology of highest weight supermodules is always non-trivial. In particular, we explicitly compute the Dirac cohomology of finite-dimensional simple supermodules for basic Lie superalgebras of type 1 with a typical highest weight, as well as of simple supermodules in the parabolic BGG category. We further investigate the relationship between Dirac cohomology and Kostant (co)homology, proving that, under suitable conditions, Dirac cohomology embeds into Kostant (co)homology. Moreover, we show that this embedding lifts to an isomorphism when the supermodule is unitarizable.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337181","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}