Communications in Mathematical Physics最新文献

{"title":"Grad-Caflisch Pointwise Decay Estimates Revisited","authors":"Ning Jiang,&nbsp;Yi-Long Luo,&nbsp;Shaojun Tang","doi":"10.1007/s00220-025-05387-2","DOIUrl":"10.1007/s00220-025-05387-2","url":null,"abstract":"<div><p>In the influential paper (Caflisch in Commun Pure Appl Math 33:651–666, 1980) which was the starting point of the employment of Hilbert expansion method to the rigorous justifications of the fluid limits of the Boltzmann equation, Caflisch discovered an elegant and crucial estimate on each expansion term (Proposition 3.1 in Caflisch (Commun Pure Appl Math 33:651–666, 198)). The proof essentially relied on an estimate of Grad as reported by Grad (in: Proceedings of the 3rd international symposium, held at the Palais de l’UNESCO, Paris, 1962), which was on the pointwise decay properties of <span>(mathcal {L}^{-1})</span>, the pseudo-inverse operator of the linearized Boltzmann collision operator <span>(mathcal {L})</span>, for the hard potential collision kernel, i.e. the power <span>(0le gamma le 1)</span>. Caflisch’s arguments need the exponential version of Grad’s estimate. However, Grad’s original paper was only on the polynomial decay. In this paper, we revisit and provide a full proof of the Caflisch-Grad type decay estimates and the corresponding applications in the compressible Euler limit of the Boltzmann equaiton. The main novelty is that for the case collision kernel power <span>(-frac{3}{2}&lt;gamma le 1)</span>, the proof of the pointwise estimate does not use any derivatives. So the potential applications of this estimate could be wider than in the Hilbert expansion. For the completeness of the result, we also prove the almost everywhere pointwise estimate using derivatives for the case <span>(-3&lt;gamma le -frac{3}{2})</span>. Furthermore, in the application to fluid limits, <span>(mathcal {L}^{-1})</span> and the derivatives with respect to the parameters (for example, (<i>t</i>, <i>x</i>), this must happen when <span>(mathcal {L})</span> is linearized around local Maxwellian which depends on (<i>t</i>, <i>x</i>)) are not commutative. We detailed analyze the estimate of commutators, which was missing in previous literatures of fluid limits of the Boltzmann equation. This estimate is needed in all compressible fluid limits from Boltzmann equation.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162230","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":"Regularity and Temperature of Stationary Black Hole Event Horizons","authors":"Raymond A. Hounnonkpe,&nbsp;Ettore Minguzzi","doi":"10.1007/s00220-025-05413-3","DOIUrl":"10.1007/s00220-025-05413-3","url":null,"abstract":"<div><p>Available proofs of the regularity of stationary black hole event horizons rely on certain assumptions on the existence of sections that imply a <span>(C^1)</span> differentiability assumption. By using a quotient bundle approach, we remedy this problem by proving directly that, indeed, under the null energy condition event horizons of stationary black holes are totally geodesic null hypersurfaces as regular as the metric. Only later, by using this result, we show that the cross-sections, whose existence was postulated in previous works, indeed exist. These results hold true under weak causality conditions. Subsequently, we prove that under the dominant energy condition stationary black hole event horizons indeed admit constant surface gravity, a result that does not require any non-degeneracy assumption, requirements on existence of cross-sections or a priori smoothness conditions. We are able to make sense of the angular velocity and of the value (not just sign) of surface gravity as quantities related to the horizon, without the need of assuming Einstein’s vacuum equations and the Killing extension. Physically, this implies that under very general conditions every stationary black hole has indeed a constant temperature (the zeroth law of black hole thermodynamics).\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162488","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":"Hawking’s Singularity Theorem for Lipschitz Lorentzian Metrics","authors":"Matteo Calisti,&nbsp;Melanie Graf,&nbsp;Eduardo Hafemann,&nbsp;Michael Kunzinger,&nbsp;Roland Steinbauer","doi":"10.1007/s00220-025-05380-9","DOIUrl":"10.1007/s00220-025-05380-9","url":null,"abstract":"<div><p>We prove Hawking’s singularity theorem for spacetime metrics of local Lipschitz regularity. The proof rests on (1) new estimates for the Ricci curvature of regularising smooth metrics that are based upon a quite general Friedrichs-type lemma and (2) the replacement of the usual focusing techniques for timelike geodesics—which in the absence of a classical ODE-theory for the initial value problem are no longer available—by a worldvolume estimate based on a segment-type inequality that allows one to control the volume of the set of points in a spacelike surface that possess long maximisers.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12316818/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144774444","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":"Entropic Fluctuations in Statistical Mechanics II. Quantum Dynamical Systems","authors":"T. Benoist,&nbsp;L. Bruneau,&nbsp;V. Jakšić,&nbsp;A. Panati,&nbsp;C.-A. Pillet","doi":"10.1007/s00220-025-05360-z","DOIUrl":"10.1007/s00220-025-05360-z","url":null,"abstract":"<div><p>The celebrated Evans–Searles, respectively Gallavotti–Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state. In this paper, we consider and compare several possible extensions of these fluctuation theorems to quantum systems. In addition to the direct two-time measurement approach whose discussion is based on Benoist et al. (Lett Math Phys 114:32, 2024. https://doi.org/10.1007/s11005-024-01777-0), we discuss a variant where measurements are performed indirectly on an auxiliary system called ancilla, and which allows to retrieve non-trivial statistical information using ancilla state tomography. We also show that modular theory provides a way to extend the classical notion of phase space contraction rate to the quantum domain, which leads to a third extension of the fluctuation theorems. We further discuss the quantum version of the principle of regular entropic fluctuations, introduced in the classical context in Jakšić et al. (Nonlinearity 24:699, 2011. https://doi.org/10.1088/0951-7715/24/3/003). Finally, we relate the statistical properties of these various notions of entropy production to spectral resonances of quantum transfer operators. The obtained results shed a new light on the nature of entropic fluctuations in quantum statistical mechanics.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05360-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145154137","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":"Boundary Driven Instabilities of Couette Flows","authors":"Dongfen Bian,&nbsp;Emmanuel Grenier,&nbsp;Nader Masmoudi,&nbsp;Weiren Zhao","doi":"10.1007/s00220-025-05401-7","DOIUrl":"10.1007/s00220-025-05401-7","url":null,"abstract":"<div><p>In this article, we prove that the threshold of instability of the classical Couette flow in <span>(H^s)</span> for large <i>s</i> is <span>(nu ^{1/2})</span>. The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of width <span>(nu ^{1/2})</span> which is itself linearly unstable. This leads to a secondary instability which in turn creates a sub-layer.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160700","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":"On Two Families of Quantum Vertex Algebras of FRT-Type","authors":"Lucia Bagnoli,&nbsp;Marijana Butorac,&nbsp;Slaven Kožić","doi":"10.1007/s00220-025-05402-6","DOIUrl":"10.1007/s00220-025-05402-6","url":null,"abstract":"<div><p>We consider two new families of quantum vertex algebras which are associated with the type <i>A</i> trigonometric <i>R</i>-matrix and elliptic <i>R</i>-matrix of the eight-vertex model. We show that their <span>(phi )</span>-coordinated representation theory is governed by the so-called FRT-operator, <i>h</i>-adically restricted operator satisfying the FRT-relation, and we demonstrate some applications of this result. Finally, in the elliptic case, we investigate the properties of the quantum determinant associated with the corresponding quantum vertex algebra.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160638","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":"Fusion 3-Categories for Duality Defects","authors":"Lakshya Bhardwaj,&nbsp;Thibault Décoppet,&nbsp;Sakura Schäfer-Nameki,&nbsp;Matthew Yu","doi":"10.1007/s00220-025-05388-1","DOIUrl":"10.1007/s00220-025-05388-1","url":null,"abstract":"<div><p>We study the fusion 3-categorical symmetries for quantum theories in (3+1)-dimensions with self-duality defects. Such defects have been realized physically by half-space gauging in theories with one-form symmetries <i>A</i>[1] for an abelian group <i>A</i>, and have found applications in the continuum and the lattice. These fusion 3-categories will be called (generalized) Tambara-Yamagami fusion 3-categories (<b>3TY</b>), in analogy to the TY fusion 1-categories. We consider the Brauer-Picard and Picard 4-groupoids to construct these categories using a 3-categorical version of the extension theory introduced by Etingof, Nikshych and Ostrik. These two 4-groupoids correspond to looking at the construction of duality defects either directly from the 4d point of view, or from the point of view of the 5d Symmetry Topological Field Theory (SymTFT). At this categorical level, the Witt group of non-degenerate braided fusion 1-categories naturally appears in the aforementioned 4-groupoids and represents enrichments of standard duality defects by (2+1)d TFTs. Our main objective is to study graded extensions of the fusion 3-category <span>(textbf{3Vect}(A[1]))</span> for some finite abelian group <i>A</i>, which is the symmetry category associated to a (3+1)d theory with 1-form symmetry <i>A</i>. Firstly, we do so explicitly using invertible bimodule 3-categories and the Brauer-Picard 4-groupoid. Secondly, we use that the Brauer-Picard 4-groupoid of <span>(textbf{3Vect}(A[1]))</span> can be identified with the Picard 4-groupoid of its Drinfeld center. Moreover, the Drinfeld center of <span>(textbf{3Vect}(A[1]))</span>, which represents topological defects of the SymTFT, is completely described by a sylleptic strongly fusion 2-category formed by topological surface defects of the SymTFT. These are classified by a finite abelian group equipped with an alternating 2-form. We relate the Picard 4-groupoid of the corresponding braided fusion 3-categories with a generalized Witt group constructed from certain graded braided fusion 1-categories using a twisted Deligne tensor product. In tractable examples, we are able to carry out explicit computations so as to understand the categorical structure of the <span>(mathbb {Z}/2)</span> and <span>(mathbb {Z}/4)</span> graded <b>3TY</b> categories.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12316798/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144774443","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":"Bihamiltonian Structure of the DR Hierarchy in the Semisimple Case","authors":"Alexandr Buryak,&nbsp;Paolo Rossi","doi":"10.1007/s00220-025-05351-0","DOIUrl":"10.1007/s00220-025-05351-0","url":null,"abstract":"<div><p>Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using the geometry of the double ramification (DR) cycle, the second has the advantage of being very explicit. The Poisson operator of the DR hierarchy is <span>(eta ^{-1} {partial }_x)</span>, where <span>(eta )</span> is the metric of the CohFT, and the Hamiltonians are explicitly defined as generating functions of intersection numbers of the CohFT with the DR cycle, the top Hodge class <span>(lambda _g)</span>, and powers of a psi-class. The question whether the DR hierarchy is endowed with a bihamiltonian structure appeared to be much harder. In our previous work in collaboration with S. Shadrin, when the CohFT is homogeneous, we proposed an explicit formula for a differential operator and conjectured that it would provide the required bihamiltonian structure. In this paper, we prove this conjecture. Our proof is based on two recently proved results: the equivalence of the DR hierarchy and the Dubrovin-Zhang hierarchy of a semisimple CohFT under Miura transformation and the polynomiality of the second Poisson bracket of the DZ hierarchy of a homogeneous semisimple CohFT. In particular, our second Poisson bracket coincides through the DR/DZ equivalence with the second Poisson bracket of the DZ hierarchy, hence providing a remarkably explicit approach to their bihamiltonian structure.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145154136","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":"Large-n asymptotics for Weil-Petersson volumes of moduli spaces of bordered hyperbolic surfaces","authors":"Will Hide,&nbsp;Joe Thomas","doi":"10.1007/s00220-025-05369-4","DOIUrl":"10.1007/s00220-025-05369-4","url":null,"abstract":"<div><p>We study the geometry and spectral theory of Weil-Petersson random surfaces with genus-<i>g</i> and <i>n</i> cusps in the large-<i>n</i> limit. We show that for a random hyperbolic surface in <span>(mathcal {M}_{g,n})</span> with <i>n</i> large, the number of small Laplacian eigenvalues is linear in <i>n</i> with high probability. By work of Otal and Rosas [42], this result is optimal up to a multiplicative constant. We also study the relative frequency of simple and non-simple closed geodesics, showing that on random surfaces with many cusps, most closed geodesics with lengths up to <span>(log (n))</span> scales are non-simple. Our main technical contribution is a novel large-<i>n</i> asymptotic formula for the Weil-Petersson volume <span>(V_{g,n}left( ell _{1},dots ,ell _{k}right) )</span> of the moduli space <span>(mathcal {M}_{g,n}left( ell _{1},dots ,ell _{k}right) )</span> of genus-<i>g</i> hyperbolic surfaces with <i>k</i> geodesic boundary components and <span>(n-k)</span> cusps with <i>k</i> fixed, building on work of Manin and Zograf [31].</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12316758/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144774445","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 (textrm{Sp}(n))-Instantons and the Fourier–Mukai Transform of Complex Lagrangians","authors":"Jesse Madnick,&nbsp;Emily Autumn Windes","doi":"10.1007/s00220-025-05389-0","DOIUrl":"10.1007/s00220-025-05389-0","url":null,"abstract":"<div><p>The real Fourier–Mukai (RFM) transform relates calibrated graphs to so-called “deformed instantons” on Hermitian line bundles. We show that under the RFM transform, complex Lagrangian graphs in <span>(mathbb {R}^{2n} times T^{2n})</span> correspond to <span>(textrm{Sp}(n))</span>-instantons over <span>(mathbb {R}^{2n} times (T^{2n})^*)</span>. In other words, the deformed <span>(textrm{Sp}(n))</span>-instanton equation coincides with the usual <span>(textrm{Sp}(n))</span>-instanton equation. Motivated by this observation, we study <span>(textrm{Sp}(n))</span>-instantons on hyperkähler manifolds <span>(X^{4n})</span>, with an emphasis on conical singularities. First, when <span>(X = C(M))</span> is a hyperkähler cone, we relate <span>(textrm{Sp}(n))</span>-instantons on <i>X</i> to tri-contact instantons on the 3-Sasakian link <i>M</i> and consider various dimensional reductions. Second, when <i>X</i> is an asymptotically conical (AC) hyperkähler manifold of rate <span>(nu le -frac{2}{3}(2n+1))</span>, we prove a Lewis-type theorem to the following effect: If the set of AC <span>(textrm{Sp}(n))</span>-instantons is non-empty, then every AC Hermitian Yang–Mills connection over <i>X</i> with sufficiently fast decay at infinity is an <span>(textrm{Sp}(n))</span>-instanton.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160521","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}