Annales Henri Poincaré最新文献

{"title":"On the Spectrum of Sturmian Hamiltonians of Bounded Type in a Small Coupling Regime","authors":"Alexandro Luna","doi":"10.1007/s00023-025-01581-z","DOIUrl":"10.1007/s00023-025-01581-z","url":null,"abstract":"<div><p>We prove that the Hausdorff dimension of the spectrum of a discrete Schrödinger operator with Sturmian potential of bounded type tends to one as coupling tends to zero. The proof is based on the trace map formalism.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 6","pages":"2155 - 2197"},"PeriodicalIF":1.3,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148208748","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":"Current Fluctuations for the Boundary-Driven Zero-Range Process on Graphs: Microscopic Versus Macroscopic Approach and a Theory of Non-reversible Resistor-Like Networks","authors":"Davide Gabrielli,&nbsp;Rosemary J. Harris","doi":"10.1007/s00023-025-01582-y","DOIUrl":"10.1007/s00023-025-01582-y","url":null,"abstract":"<div><p>We compute the joint large deviation rate functional in the limit of large time for the current flowing through the edges of a finite graph on which a boundary-driven system of stochastic particles evolves with zero-range dynamics. This generalizes one-dimensional results previously obtained with different approaches (Bertini et al. in J Stat Phys 123(2):237–276, 2006; Harris et al. in J Stat Mech Theory Exp 2005:P08003, 2005); our alternative techniques illuminate various connections and complementary perspectives. In particular, we here use a variational approach to derive the rate functional by contraction from a level 2.5 large deviation rate functional. We perform an exact minimization and finally obtain the rate functional as a variational problem involving a superposition of cost functions for each edge. The contributions from different edges are not independent since they are related by the values of a potential function on the nodes of the graph. The rate functional on the graph is a microscopic version of the continuous rate functional predicted by the macroscopic fluctuation theory (Bertini et al. in Rev Mod Phys 87(2):593–636, 2015), and we indeed show a convergence in the scaling limit. If we split the graph into two connected regions by a cutset and are interested just in the current flowing through the cutset, we find that the result is the same as that of an effective system composed of only one effective edge [as happens at macroscopic level and is expected also for other models (Akkermans et al. in Europhys Lett 103(2):20001, 2013)]. The characteristics of this effective edge are related to the “capacities” of the graph and can be obtained by a reduction using elementary transformations as in electrical networks; specifically, we treat components in parallel, in series, and in <i>N</i>-star configurations (reduced to effective complete <i>N</i>-graphs). Our reduction procedure is directly related to the reduction to the trace process (Landim in Probab Surv 16:143–227, 2019) and, since the dynamics is in general not reversible, it is also closely connected to the theory of non-reversible electrical networks in Balázs and Folly (Am Math Mon 123(7):657–682, 2016).</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 7","pages":"2605 - 2647"},"PeriodicalIF":1.4,"publicationDate":"2025-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-025-01582-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458664","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":"Pfaffian Structure of the Eigenvector Overlap for the Symplectic Ginibre Ensemble","authors":"Gernot Akemann,&nbsp;Sung-Soo Byun,&nbsp;Kohei Noda","doi":"10.1007/s00023-025-01575-x","DOIUrl":"10.1007/s00023-025-01575-x","url":null,"abstract":"<div><p>We study the integrable structure and scaling limits of the conditioned eigenvector overlap of the symplectic Ginibre ensemble of Gaussian non-Hermitian random matrices with independent quaternion elements. The average of the overlap matrix elements constructed from left and right eigenvectors, conditioned to <i>x</i>, are derived in terms of a Pfaffian determinant. Regarded as a two-dimensional Coulomb gas with the Neumann boundary condition along the real axis, it contains a kernel of skew-orthogonal polynomials with respect to the weight function <span>(omega ^mathrm{(over)}(z)=|z-overline{x}|^2(1+|z-x|^2)e^{-2|z|^2})</span>, so including a non-trivial insertion of a point charge. The mean off-diagonal overlap is related to the diagonal (self-)overlap by a transposition, in analogy to the complex Ginibre ensemble. For <i>x</i> conditioned to the real line, extending previous results at <span>(x=0)</span>, we determine the skew-orthogonal polynomials and their skew-kernel with respect to <span>(omega ^mathrm{(over)}(z))</span>. This is done in two steps and involves a Christoffel perturbation of the weight <span>(omega ^mathrm{(over)}(z)=|z-overline{x}|^2omega ^mathrm{(pre)}(z))</span>, by computing first the corresponding quantities for the unperturbed weight <span>(omega ^mathrm{(pre)}(z))</span>. Its kernel is shown to satisfy a differential equation at finite matrix size <i>N</i>. This allows us to take different large-<i>N</i> limits, where we distinguish bulk and edge regime along the real axis. The limiting mean diagonal overlaps and corresponding eigenvalue correlation functions of the point processes with respect to <span>(omega ^mathrm{(over)}(z))</span> are determined. We also examine the effect on the planar orthogonal polynomials when changing the variance in <span>(omega ^mathrm{(pre)}(z))</span>, as this appears in the eigenvector statistics of the complex Ginibre ensemble.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 4","pages":"1207 - 1258"},"PeriodicalIF":1.3,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-025-01575-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686531","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":"Spectral Regularity and Defects for the Kohmoto Model","authors":"Siegfried Beckus,&nbsp;Jean Bellissard,&nbsp;Yannik Thomas","doi":"10.1007/s00023-025-01578-8","DOIUrl":"10.1007/s00023-025-01578-8","url":null,"abstract":"<div><p>We study the Kohmoto model including Sturmian Hamiltonians and the associated Kohmoto butterfly. We prove spectral estimates for the operators using Farey numbers. In addition, we determine the impurities at rational rotations leading to the spectral defects in the Kohmoto butterfly. Our results are similar to the ones obtained for the almost-Mathieu operator and the associated Hofstadter butterfly.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 6","pages":"2117 - 2154"},"PeriodicalIF":1.3,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-025-01578-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148208751","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":"Boundary Conditions and Violations of Bulk-Edge Correspondence in a Hydrodynamic Model","authors":"Gian Michele Graf,&nbsp;Alessandro Tarantola","doi":"10.1007/s00023-025-01577-9","DOIUrl":"10.1007/s00023-025-01577-9","url":null,"abstract":"<div><p>Bulk-edge correspondence is a wide-ranging principle that applies to topological matter, as well as a precise result established in a large and growing number of cases. According to the principle, the distinctive topological properties of matter, thought of as extending indefinitely in space, are equivalently reflected in the excitations running along its boundary, when one is present. Indices encode those properties, and their values, when differing, are witness to a violation of that correspondence. We address such violations, as they are encountered in a hydrodynamic context. The model concerns a shallow layer of fluid in a rotating frame and provides a local description of waves propagating either across the oceans or along a coastline; it becomes topological when suitably modified at short distances. The edge index is sensitive to boundary conditions, as exemplified in earlier work, hence exhibiting a violation. Here we present classification of all (local, self-adjoint) boundary conditions and a parameterization of their manifold. They come in four families, distinguished in part by the degree of their underlying differential operators. Essentially, that degree counts the degrees of freedom of the hydrodynamic field that are constrained at the boundary by way of their normal derivatives. Generally, both the correspondence and its violation are typical. Within families though, the maximally possible amount of violation is increasing with its degree. Several indices of interest are charted for all boundary conditions. A single spectral mechanism for the onset of violations is furthermore identified. The role of a symmetry is investigated.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 2","pages":"453 - 527"},"PeriodicalIF":1.3,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-025-01577-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337785","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":"The Backscattering Problem for Time-Dependent Potentials","authors":"Medet Nursultanov,&nbsp;Lauri Oksanen,&nbsp;Plamen Stefanov","doi":"10.1007/s00023-025-01579-7","DOIUrl":"10.1007/s00023-025-01579-7","url":null,"abstract":"<div><p>We study the inverse backscattering problem for time-dependent potentials. We prove uniqueness and Lipschitz stability for the recovery of small potentials.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 6","pages":"2041 - 2071"},"PeriodicalIF":1.3,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-025-01579-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148208764","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":"Conservation Law and Trace Anomaly for the Stress-Energy Tensor of a Self-interacting Scalar Field","authors":"Beatrice Costeri,&nbsp;Claudio Dappiaggi,&nbsp;Michele Goi","doi":"10.1007/s00023-025-01580-0","DOIUrl":"10.1007/s00023-025-01580-0","url":null,"abstract":"<div><p>We consider a self-interacting, massive, real scalar field on a four-dimensional globally hyperbolic spacetime and the associated stress-energy tensor. Using techniques proper of the algebraic approach to perturbative quantum field theory, we study the associated, Wick-ordered, quantum observable. In particular, we generalize a construction, first developed in the free field theory scenario by Moretti in (Commun Math Phys 232: 189–221, 2003. arXiv:gr-qc/0109048 [gr-qc]), aimed at exploiting the existing freedoms in the definition of the classical stress-energy tensor, in order to define a quantum counterpart which is divergence free. We focus on Minkowski spacetime proving that this procedure can be adapted also to cubic or quartic self-interactions, at least up to order <span>({mathcal {O}}(lambda ^3))</span> in perturbation theory. We remark that this result can be extended to arbitrary globally hyperbolic spacetimes, although in this case one needs to exploit the existing regularization freedom in the construction of the Wick ordered stress-energy tensor.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 5","pages":"1843 - 1884"},"PeriodicalIF":1.3,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-025-01580-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147872275","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":"Dirichlet Scalar Determinants on Two-Dimensional Constant Curvature Disks","authors":"Soumyadeep Chaudhuri,&nbsp;Frank Ferrari","doi":"10.1007/s00023-025-01576-w","DOIUrl":"10.1007/s00023-025-01576-w","url":null,"abstract":"<div><p>We compute the scalar determinants <span>(det (Delta +M^{2}))</span> on the two-dimensional round disks of constant curvature <span>(R=0)</span>, <span>({mp } 2)</span>, for any finite boundary length <span>(ell )</span> and mass <i>M</i>, with Dirichlet boundary conditions, using the <span>(zeta )</span>-function prescription. When <span>(M^{2}=pm q(q+1))</span>, <span>(qin {mathbb {N}})</span>, a simple expression involving only elementary functions and the Euler <span>(Gamma )</span> function is found. Applications to two-dimensional Liouville and Jackiw–Teitelboim quantum gravity are presented in a separate paper.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 6","pages":"2003 - 2039"},"PeriodicalIF":1.3,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148208746","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":"Ambitwistor Yang–Mills Theory Revisited","authors":"Leron Borsten,&nbsp;Branislav Jurčo,&nbsp;Hyungrok Kim,&nbsp;Christian Saemann,&nbsp;Martin Wolf","doi":"10.1007/s00023-025-01572-0","DOIUrl":"10.1007/s00023-025-01572-0","url":null,"abstract":"<div><p>Inspired by the Movshev–Mason–Skinner Cauchy–Riemann (CR) ambitwistor approach, we provide a rigorous yet elementary construction of a twisted CR holomorphic Chern–Simons action on CR ambitwistor space for maximally supersymmetric Yang–Mills theory on four- dimensional Euclidean space. The key ingredient in our discussion is the homotopy algebraic perspective on perturbative quantum field theory. Using this technology, we show that both theories are semi-classically equivalent, that is, we construct a quasi-isomorphism between the cyclic <span>(L_infty )</span>-algebras governing both field theories. This confirms a conjecture from the literature. Furthermore, we also show that the Yang–Mills action is obtained by integrating out an infinite tower of auxiliary fields in the Chern–Simons action, that is, the two theories are related by homotopy transfer. Given its simplicity, this Chern–Simons action should form a fruitful starting point for analysing perturbative properties of Yang–Mills theory.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 5","pages":"1755 - 1795"},"PeriodicalIF":1.3,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-025-01572-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147872274","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":"Gibbs Scheme in the Theory of Random Fields","authors":"Linda A. Khachatryan,&nbsp;Boris S. Nahapetian","doi":"10.1007/s00023-025-01573-z","DOIUrl":"10.1007/s00023-025-01573-z","url":null,"abstract":"<div><p>The purpose of this work is to expand and clarify the concept of the class of Gibbs random fields and give its structure the form accepted in the theory of random processes. This is possible thanks to the proposed purely probabilistic definition of the Gibbs random field without referring to any physical notion. However, we do not oppose to each other the physical and probabilistic points of view on mathematical statistical physics; on the contrary, we show their natural compatibility within the framework of the suggested Gibbs scheme. The outlines of the corresponding theory are presented. In this theory, the DLR–definition is not used. At the same time, the related existence theorem provides one adequate way to construct Gibbs random fields (in the sense of our, purely probabilistic definition). The results of mathematical statistical physics are embedded in the theory of Gibbs random fields under development as an important (if not the most important) part. We describe in general terms the range of those problems that are more natural to solve using our definition. For example, the problem of the Gibbsian description of known classes of random fields as well as questions of validity of limit theorems of probability theory.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 6","pages":"2341 - 2367"},"PeriodicalIF":1.3,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148208763","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}