Communications in Mathematical Physics最新文献

{"title":"Well-Posedness of the Stochastic Thin-Film Equation with an Interface Potential","authors":"Antonio Agresti,&nbsp;Max Sauerbrey","doi":"10.1007/s00220-026-05563-y","DOIUrl":"10.1007/s00220-026-05563-y","url":null,"abstract":"<div><p>We consider strictly positive solutions to a class of fourth-order conservative quasilinear SPDEs on the <i>d</i>-dimensional torus modeled after the stochastic thin-film equation. We prove local Lipschitz estimates in Bessel potential spaces under minimal assumptions on the parameters and corresponding stochastic maximal <span>(L^p)</span>-regularity estimates for thin-film type operators with measurable in time coefficients. As a result, we deduce local well-posedness of the stochastic thin-film equation as well as blow-up criteria and instantaneous regularization for the solution. In dimension one, we additionally close <span>(alpha )</span>-entropy estimates and subsequently an energy estimate for the stochastic thin-film equation with an interface potential so that global well-posedness follows. We allow for a wide range of mobility functions, including the power laws <span>(u^n)</span> for <span>(nin [0,6))</span> as long as the interface potential is sufficiently repulsive.</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://www.ncbi.nlm.nih.gov/pmc/articles/PMC13350212/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148417572","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":"Non-resonant Hopf Links near a Hamiltonian Equilibrium Point","authors":"C. Grotta-Ragazzo,&nbsp;Lei Liu,&nbsp;Pedro A. S. Salomão","doi":"10.1007/s00220-026-05650-0","DOIUrl":"10.1007/s00220-026-05650-0","url":null,"abstract":"<div><p>This paper is about the existence of periodic orbits near an equilibrium point of a two-degree-of-freedom Hamiltonian system. The equilibrium is supposed to be a nondegenerate minimum of the Hamiltonian. Every sphere-like component of the energy surface sufficiently close to the equilibrium contains at least two periodic orbits forming a Hopf link (Weinstein in Inv Math 20:47–57, 1973). A theorem by Hofer, Wysocki and Zehnder (Ann Math 148:197–289, 1998) implies that there are either precisely two or infinitely many periodic orbits on such a component of the energy surface. This multiplicity result follows from the existence of a disk-like global surface of section. If a certain non-resonance condition on the rotation numbers of the orbits of the Hopf link is satisfied, then by Hryniewicz, Momin and Salomão (Inv Math 199:333–422, 2015), infinitely many periodic orbits follow. This paper aims to present explicit conditions on the Birkhoff-Gustavson normal forms of the Hamiltonian function at the equilibrium point that ensure the existence of infinitely many periodic orbits on the energy surface by checking the non-resonance condition as in (Hryniewicz, Momin and Salomão in Inv Math 199:333–422, 2015) and not making use of any global surface of section. The main results apply to the Spatial Isosceles Three-Body Problem, Hill’s Lunar Problem, and the Hénon-Heiles System, where non-resonant Hopf links are proved to exist.\u0000</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":"148433506","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":"Annealed and Quenched Representations of the Gauss–Rényi Measure by “Periodic Points”","authors":"Shintaro Suzuki,&nbsp;Hiroki Takahasi","doi":"10.1007/s00220-026-05667-5","DOIUrl":"10.1007/s00220-026-05667-5","url":null,"abstract":"<div><p>We study independently identically distributed random compositions of the Gauss and Rényi maps that are related to Diophantine approximation. Elaborating on methods in ergodic theory, thermodynamic formalism and large deviations, we prove that weighted cycles of this random dynamical system equidistribute with respect to the Gauss–Rényi measure. We obtain both annealed (sample-averaged) and quenched (samplewise) results.</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":"148433573","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":"Invariants from Involutory Hopf Algebras of 3-Manifolds with Embedded Framed Links","authors":"Nicolas Bridges,&nbsp;Shawn X. Cui","doi":"10.1007/s00220-026-05683-5","DOIUrl":"10.1007/s00220-026-05683-5","url":null,"abstract":"<div><p>We give invariants of pairs (<i>M</i>, <i>L</i>) consisting of a closed connected oriented three-manifold and an (oriented) framed link <i>L</i> embedded in <i>M</i>. This invariant generalizes the Kuperberg and Hennings-Kauffman-Radford (HKR) invariants of three-manifolds. We define Heegaard-Link diagrams which represent the pair (<i>M</i>, <i>L</i>) and use the data of an involutory Hopf algebra and a representation of the Drinfeld double to construct the invariant. We show that if <i>L</i> is the empty link, then the invariant recovers the Kuperberg invariant, and if <i>M</i> is the three-sphere and certain particular representation is chosen, then the invariant recovers the HKR invariant. We also show that if the representation is the left regular representation of the Drinfeld double, then we recover the Kuperberg invariant of the surgery manifold <i>M</i>(<i>L</i>), contributing to a new proof of the relationship between the HKR and Kuperberg invariants in the semisimple setting. To this end, we give a Heegaard diagram for <i>M</i>(<i>L</i>) coming from the Heegaard-Link diagram representing the pair (<i>M</i>, <i>L</i>). We also introduce a colored link invariant extending the construction and show it recovers the Reshetikhin-Turaev colored link invariant.</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/s00220-026-05683-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433575","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 the Past Maximal Development of Near-FLRW Data for the Einstein Scalar-Field Vlasov System","authors":"David Fajman,&nbsp;Liam Urban","doi":"10.1007/s00220-026-05635-z","DOIUrl":"10.1007/s00220-026-05635-z","url":null,"abstract":"<div><p>We show that the maximal globally hyperbolic development of near-FLRW initial data for the Einstein scalar-field Vlasov system exhibits stable Big Bang formation in the collapsing direction. The solutions exhibit stable Kretschmann scalar blow-up, causing the spacetime to become causally geodesically past incomplete, and are asymptotically velocity term dominated. This is the first stability result for the Einstein equations in the collapsing spacetime direction in presence of Vlasov matter that does not rely on any symmetry assumptions. Furthermore, the Vlasov distribution remains close to that of the FLRW solution as a function on the co-mass shell, and so does its momentum support if one assumes it to be close to that of the FLRW distribution initially. On the other hand, the leading order terms in components of the Vlasov energy-momentum tensor exbihit an offset in asymptotic order controlled by the perturbation size, and when viewed on the mass shell, the distribution asymptotically concentrates in certain preferred velocity directions. To ensure that this behaviour is sufficiently mitigated by the scalar field, we crucially exploit a scaling hierarchy between horizontal and vertical derivatives in the commuted Vlasov equation.</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://www.ncbi.nlm.nih.gov/pmc/articles/PMC13350106/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148417547","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 New Look at Unitarity in Quantization Commutes with Reduction for Toric Manifolds","authors":"J. M. Mourão,&nbsp;João P. Nunes,&nbsp;Augusto Pereira,&nbsp;Dan Wang","doi":"10.1007/s00220-026-05685-3","DOIUrl":"10.1007/s00220-026-05685-3","url":null,"abstract":"<div><p>For a symplectic manifold <i>M</i> with the Hamiltonian action of a compact Lie group <i>G</i>, we give a new perspective on the problem of unitarity in the quantization commutes with reduction correspondence. We argue that this correspondence leads naturally to the introduction of what we call Fourier polarizations, whose real directions include the Hamiltonian vector fields of all invariant functions of the moment map. For a Fourier polarization, quantization commutes with reduction unitarily. For a general <i>G</i>-invariant polarization, <span>(mathcal {P})</span>, unitarity in the quantization commutes with reduction correspondence can then be formulated in terms of the existence of a Fourier polarization, <span>(mathcal {P}_F)</span>, such that the quantizations with respect to <span>(mathcal {P})</span> and to <span>(mathcal {P}_F)</span> are unitarily equivalent. We describe this perspective in detail for symplectic toric manifolds, by considering symplectic reductions associated to the action of a subtorus <span>(T^psubset T^n)</span>. We consider half-form quantization in Fourier (mixed) polarizations <span>(mathcal {P}_infty )</span>, whose real directions are generated by (the Hamiltonian vector fields of the) components of the <span>(T^p)</span> moment map. We show that Fourier mixed polarizations of this type can be obtained by Mabuchi geodesic rays of toric Kähler structures, starting at a given initial structure and with velocity given by the norm square of the moment map of the torus subgroup. We lift these geodesic rays to the quantum bundle via generalized coherent state transforms, which define equivariant isomorphisms between quantum Hilbert spaces for the Kähler and Fourier polarizations, where the later are obtained at infinite geodesic time. Unitarity in quantization commutes with reduction in these cases then becomes equivalent to the unitarity of these isomorphisms. In general, however, in the toric case, these isomorphisms are not unitary.</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/s00220-026-05685-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433508","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":"Third Order Upper Bound for the Ground State Energy of the Dilute Bose Gas","authors":"Morris Brooks,&nbsp;Jakob Oldenburg,&nbsp;Diane Saint Aubin,&nbsp;Benjamin Schlein","doi":"10.1007/s00220-026-05656-8","DOIUrl":"10.1007/s00220-026-05656-8","url":null,"abstract":"<div><p>We consider a dilute Bose gas in the thermodynamic limit. We prove an upper bound for the ground state energy per unit volume, capturing the expected third order term, as predicted by Wu, Hugenholtz–Pines and Sawada.</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":"148433568","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":"Mixing Rate Exponent of Planar Fortuin-Kasteleyn Percolation","authors":"Haoyu Liu,&nbsp;Baojun Wu,&nbsp;Zijie Zhuang","doi":"10.1007/s00220-026-05693-3","DOIUrl":"10.1007/s00220-026-05693-3","url":null,"abstract":"<div><p>Duminil-Copin and Manolescu [6] recently proved the scaling relations for planar Fortuin-Kasteleyn (FK) percolation. In particular, they showed that the one-arm exponent and the mixing rate exponent are sufficient to derive the other near-critical exponents. The scaling limit of critical FK percolation is conjectured to be a conformally invariant random collection of loops called the conformal loop ensemble (CLE). In this paper, we define the CLE analog of the mixing rate exponent. Assuming the convergence of FK percolation to CLE, we show that the mixing rate exponent for FK percolation agrees with that of CLE. We prove that the CLE<span>(_kappa )</span> mixing rate exponent equals <span>(frac{3 kappa }{8}-1)</span>, thereby answering Question 3 of Duminil-Copin and Manolescu [6]. The derivation of the CLE exponent is based on an exact formula for the Radon-Nikodym derivative between the marginal laws of the odd-level and even-level CLE loops, which is obtained from the coupling between Liouville quantum gravity and CLE.</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":"148433504","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":"Cyclic Quantum Teichmüller Theory","authors":"Tsukasa Ishibashi","doi":"10.1007/s00220-026-05604-6","DOIUrl":"10.1007/s00220-026-05604-6","url":null,"abstract":"<div><p>Based on the pioneering ideas of Kashaev (Kashaev RM, Lett. Math. 2247 Phys. 43(2), 105–115 (1998)), we present a fully explicit construction of a finite-dimensional projective representation of the dotted Ptolemy groupoid when the quantum parameter <i>q</i> is a root of unity, which reproduces the central charge of the <i>SU</i>(2) Wess–Zumino–Witten model. A basic ingredient is the cyclic quantum dilogarithm (Faddeev LD, Kashaev RM, Modern Phys. Lett. A 9(5), 427–434 2210 (1994)). A notable contribution of this work is a reinterpretation of the relations among the parameters in the cyclic quantum dilogarithm to ensure its pentagon identity in terms of the <i>mutations of coefficients</i>. In particular, we find the dual roles of these parameters: as coefficients in quantum cluster algebras and as the central characters of quantum cluster variables. We also provide a geometric method to decompose the space of quantum states into irreducible modules of the Chekhov–Fock algebra. We introduce two versions of quantum intertwiners associated with a mapping class: on the entire representation space and on each irreducible component, each being an explicit composite of cyclic quantum dilogarithm operators. We prove that the former gives an intertwiner of local representations of quantum Teichmüller space in the sense of Bai–Bonahon–Liu Bai et al., Local representations of the quantum Teichmüller space and also coincides with the transpose of the reduced quantum hyperbolic operator of Baseilhac–Benedetti (Baseilhac S, Benedetti R, Geom. Dedicata. <b>197</b>, 1–32 (2018)). The mutation relation of coefficients is equivalent to the quantum gluing equation. The irreducible intertwiner conjecturally coincides with the Bonahon–Liu intertwiner (Bonahon F, Liu X, Geom. Topol. <b>11</b>, 889–937 (2007)), and we give a partial evidence.</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/s00220-026-05604-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433505","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":"Global Minimality of the Hopf Map in the Faddeev–Skyrme Model with Large Coupling Constant","authors":"André Guerra,&nbsp;Xavier Lamy,&nbsp;Konstantinos Zemas","doi":"10.1007/s00220-026-05702-5","DOIUrl":"10.1007/s00220-026-05702-5","url":null,"abstract":"<div><p>We prove that, modulo rigid motions, the Hopf map is the unique minimizer of the Faddeev–Skyrme energy in its homotopy class, provided that the radius of the target 2-sphere is not smaller than the radius of the domain 3-sphere.</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/s00220-026-05702-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433510","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}