Annales Henri Poincaré最新文献

{"title":"Fine Structure of Flat Bands in a Chiral Model of Magic Angles","authors":"Simon Becker,&nbsp;Tristan Humbert,&nbsp;Maciej Zworski","doi":"10.1007/s00023-024-01478-3","DOIUrl":"10.1007/s00023-024-01478-3","url":null,"abstract":"<div><p>We analyse symmetries of Bloch eigenfunctions at magic angles for the Tarnopolsky–Kruchkov–Vishwanath chiral model of the twisted bilayer graphene (TBG) following the framework introduced by Becker–Embree–Wittsten–Zworski. We show that vanishing of the first Bloch eigenvalue away from the Dirac points implies its vanishing at all momenta, that is, the existence of a flat band. We also show how the multiplicity of the flat band is related to the nodal set of the Bloch eigenfunctions. We conclude with two numerical observations about the structure of flat bands.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 8","pages":"2827 - 2857"},"PeriodicalIF":1.3,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01478-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165629","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":"Discontinuities Cause Essential Spectrum on Surfaces","authors":"Oliver Butterley,&nbsp;Giovanni Canestrari,&nbsp;Roberto Castorrini","doi":"10.1007/s00023-024-01499-y","DOIUrl":"10.1007/s00023-024-01499-y","url":null,"abstract":"<div><p>Two-dimensional maps with discontinuities are considered. It is shown that, in the presence of discontinuities, the essential spectrum of the transfer operator is large whenever it acts on a Banach space with norm that is stronger than <span>(L^infty )</span> or <span>(BV)</span>. Three classes of examples are introduced and studied, both expanding and partially expanding. In two dimensions, there is complication due to the geometry of the discontinuities, an issue not present in the one-dimensional case and which is explored in this work.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 9","pages":"3075 - 3101"},"PeriodicalIF":1.3,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01499-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990638","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":"Magnetic Response Properties of Twisted Bilayer Graphene","authors":"Simon Becker,&nbsp;Jihoi Kim,&nbsp;Xiaowen Zhu","doi":"10.1007/s00023-024-01497-0","DOIUrl":"10.1007/s00023-024-01497-0","url":null,"abstract":"<div><p>In this article, we analyze the Bistritzer–MacDonald model (also known as the continuum model) of twisted bilayer graphene with an additional external magnetic field. We provide an explicit semiclassical asymptotic expansion of the density of states (DOS) in the limit of strong magnetic fields. We find that unlike for magnetic Schrödinger operators, perturbation of the chiral potentials do not expand the Landau bands while perturbations by the anti-chiral potentials do. The explicit expansion of the DOS also enables us to study magnetic response properties such as magnetic oscillations which includes Shubnikov-de Haas and de Haas-van Alphen oscillations as well as the integer quantum Hall effect.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 10","pages":"3533 - 3578"},"PeriodicalIF":1.3,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145204687","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":"Symmetric Functions from the Six-Vertex Model in Half-Space","authors":"Alexandr Garbali,&nbsp;Jan de Gier,&nbsp;William Mead,&nbsp;Michael Wheeler","doi":"10.1007/s00023-024-01484-5","DOIUrl":"10.1007/s00023-024-01484-5","url":null,"abstract":"<div><p>We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families of multivariate rational symmetric functions. Using commutation relations between double-row operators, we prove a skew Cauchy identity of these functions. In a certain degeneration of the right-hand side of the Cauchy identity we obtain the partition function of the six-vertex model in a half-quadrant, and give a Pfaffian formula for this quantity. The Pfaffian is a direct generalization of a formula obtained by Kuperberg in his work on symmetry classes of alternating-sign matrices. One of our families of symmetric functions admits an integral (sum over residues) formula, and we use this to conjecture an orthogonality property of the dual family. We conclude by studying the reduction of our integral formula to transition probabilities of the (initially empty) asymmetric simple exclusion process on the half-line.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 7","pages":"2557 - 2624"},"PeriodicalIF":1.3,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162222","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":"Semiclassical Equivalence of Two White Dwarf Models as Ground States of the Relativistic Hartree–Fock and Vlasov–Poisson energies","authors":"Younghun Hong,&nbsp;Sangdon Jin,&nbsp;Jinmyoung Seok","doi":"10.1007/s00023-024-01494-3","DOIUrl":"10.1007/s00023-024-01494-3","url":null,"abstract":"<div><p>We are concerned with the semi-classical limit for ground states of the relativistic Hartree–Fock energies (HF) under a mass constraint, which are considered as the quantum mean-field model of white dwarfs (Lenzmann and Lewin in Duke Math J 152:257–315, 2010). In Jang and Seok (Kinet Relat Models 15:605–620, 2022), fermionic ground states of the relativistic Vlasov–Poisson energy (VP) are constructed as a classical mean-field model of white dwarfs, and are shown to be equivalent to the classical Chandrasekhar model. In this paper, we prove that as the reduced Planck constant <span>(hbar )</span> goes to the zero, the <span>(hbar )</span>-parameter family of the ground energies and states of (HF) converges to the fermionic ground energy and state of (VP) with the same mass constraint.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 7","pages":"2625 - 2653"},"PeriodicalIF":1.3,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01494-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171529","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":"A Lower Semicontinuous Time Separation Function for (C^0) Spacetimes","authors":"Eric Ling","doi":"10.1007/s00023-024-01490-7","DOIUrl":"10.1007/s00023-024-01490-7","url":null,"abstract":"<div><p>The time separation function (or Lorentzian distance function) is a fundamental tool used in Lorentzian geometry. For smooth spacetimes it is known to be lower semicontinuous, and, in fact, continuous for globally hyperbolic spacetimes. Moreover, an axiom for Lorentzian length spaces—a synthetic approach to Lorentzian geometry—is the existence of a lower semicontinuous time separation function. Nevertheless, the usual time separation function is <i>not</i> necessarily lower semicontinuous for <span>(C^0)</span> spacetimes due to bubbling phenomena. In this paper, we introduce a class of curves called “nearly timelike” and show that the time separation function for <span>(C^0)</span> spacetimes is lower semicontinuous when defined with respect to nearly timelike curves. Moreover, this time separation function agrees with the usual one when the metric is smooth. Lastly, sufficient conditions are found guaranteeing the existence of nearly timelike maximizers between two points in a <span>(C^0)</span> spacetime.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 7","pages":"2293 - 2313"},"PeriodicalIF":1.3,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01490-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170483","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":"Dynamics of Mean-Field Fermi Systems with Nonzero Pairing","authors":"Stefano Marcantoni,&nbsp;Marcello Porta,&nbsp;Julien Sabin","doi":"10.1007/s00023-024-01473-8","DOIUrl":"10.1007/s00023-024-01473-8","url":null,"abstract":"<div><p>We study the dynamics of many-body Fermi systems, for a class of initial data which are close to quasi-free states exhibiting a nonvanishing pairing matrix. We focus on the mean-field scaling, which for fermionic systems is naturally coupled with a semiclassical scaling. Under the assumption that the initial datum enjoys a suitable semiclassical structure, we give a rigorous derivation of the time-dependent Hartree-Fock-Bogoliubov equation, a nonlinear effective evolution equation for the generalized one-particle density matrix of the system, as the number of particles goes to infinity. Our result holds for all macroscopic times, and provides bounds for the rate of convergence.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 8","pages":"2901 - 2954"},"PeriodicalIF":1.3,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12313753/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144777036","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":"A New Gauge for Gravitational Perturbations of Kerr Spacetimes I: The Linearised Theory","authors":"Gabriele Benomio","doi":"10.1007/s00023-024-01472-9","DOIUrl":"10.1007/s00023-024-01472-9","url":null,"abstract":"<div><p>We propose a new geometric framework to address the stability of the Kerr solution to gravitational perturbations in the full sub-extremal range <span>(|a|&lt;M)</span>. Central to our framework is a new formulation of nonlinear gravitational perturbations of Kerr, whose two novel ingredients are the choice of a geometric gauge and non-integrable null frames both tailored to the <i>outgoing principal null geodesics</i> of Kerr. The vacuum Einstein equations for the perturbations are formulated in our gauge as a system of equations for the connection coefficients and curvature components relative to the chosen frames. When renormalised with respect to Kerr, the null structure equations with the form of <i>outgoing</i> transport equations do <i>not</i> possess any derivatives of renormalised connection coefficients on the right hand side. In this work, we derive the linearised vacuum Einstein equations around Kerr in the new framework. The system of linearised gravity exhibits two key structural properties. The first is well-known and consists of the exact decoupling of two <i>gauge invariant</i> linearised quantities in the system, satisfying two decoupled spin <span>(pm , 2)</span> Teukolsky equations. The second is a <i>new</i>, <i>gauge dependent</i> structure in the <i>outgoing</i> transport equations for the linearised connection coefficients inherited from the nonlinear system: Unlike previous works, these equations do <i>not</i> contain any derivatives of linearised connection coefficients on the right hand side and induce a <i>new hierarchy</i> of only outgoing transport equations including all gauge dependent linearised quantities. Our new framework is designed to effectively capture the stabilising properties of the <i>red-shifted</i> transport equations, thereby isolating one of the crucial structures of the problem. Such a feature is suggestive of future simplifications in the analysis. As an illustration, our companion work (Benomio in A new gauge for gravitational perturbations of Kerr spacetimes II: The linear stability of Schwarzschild revisited, 2022) employs the system of linearised gravity and its enhanced red-shifted transport equations, specialised to the <span>(|a|=0)</span> case, to produce a new simplified proof of linear stability of the Schwarzschild solution. The full linear stability analysis in the full sub-extremal range <span>(|a|&lt;M)</span> is deferred to future work. As already apparent from (Benomio 2022), our framework will allow to combine the new structure in the transport equations with the elliptic part of the system to establish a linear orbital stability result <i>without loss of derivatives</i>, indicating that the framework may be well suited to address nonlinear stability in the full sub-extremal range <span>(|a|&lt;M)</span>.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 5","pages":"1573 - 1731"},"PeriodicalIF":1.4,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01472-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925486","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":"A Construction of Approximately Self-Similar Naked Singularities for the Spherically Symmetric Einstein-Scalar Field System","authors":"Jaydeep Singh","doi":"10.1007/s00023-024-01489-0","DOIUrl":"10.1007/s00023-024-01489-0","url":null,"abstract":"<div><p>In this work, we identify stable perturbations of <i>k</i>-self-similar naked singularities, in the full parameter range <span>(k^2 in (0, frac{1}{3}).)</span> As a consequence, we provide a dynamical construction of naked singularity interior and exterior regions outside of exact self-similarity, extending the work of Chrisotodoulou (Ann Math 140:607–653, 1994). More generally, we consider a wide range of singular spacetimes satisfying self-similar bounds, and parameterize perturbations in terms of fine-tuned data for the scalar field along the past lightcone of the singularity. This data is required to satisfy conditions consistent with the absence of a blue-shift instability and is therefore non-generic. The argument combines a backwards stability argument in the interior region with a global existence problem in the exterior region, adapting techniques developed by Rodnianski and Shlapentokh-Rothman (Naked singularities for the Einstein vacuum equations: the exterior solution. arXiv:1912.08478. 2019) to the spherically symmetric setting.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 7","pages":"2355 - 2465"},"PeriodicalIF":1.3,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169884","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":"Global Stability of the Open Milne Spacetime","authors":"Jinhua Wang,&nbsp;Wei Yuan","doi":"10.1007/s00023-024-01491-6","DOIUrl":"10.1007/s00023-024-01491-6","url":null,"abstract":"<div><p>The open Milne cosmological spacetime has a 3-dimensional Cauchy surface isometric to the (non-compact) hyperbolic space. We prove the globally nonlinear stability of the open Milne spacetime for both massive and massless Einstein-scalar field equations and show that as time goes to infinity, the spatial metric tends to the hyperbolic metric. The proof is based on the Gaussian normal coordinates, in which the decay rates of gravity are determined by the expanding geometry of Milne spacetime.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 7","pages":"2467 - 2504"},"PeriodicalIF":1.3,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167927","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}