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Tunneling Estimates for Two-Dimensional Perturbed Magnetic Dirac Systems 二维扰动磁性狄拉克系统的隧道估计值
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-09-05 DOI: 10.1007/s00023-024-01480-9
Esteban Cárdenas, Benjamín Pavez, Edgardo Stockmeyer
{"title":"Tunneling Estimates for Two-Dimensional Perturbed Magnetic Dirac Systems","authors":"Esteban Cárdenas,&nbsp;Benjamín Pavez,&nbsp;Edgardo Stockmeyer","doi":"10.1007/s00023-024-01480-9","DOIUrl":"10.1007/s00023-024-01480-9","url":null,"abstract":"<div><p>We prove tunneling estimates for two-dimensional Dirac systems which are localized in space due to the presence of a magnetic field. The Hamiltonian driving the motion admits the decomposition <span>( H = H_0 + W)</span>, where <span>(H_0 )</span> is a rotationally symmetric magnetic Dirac operator and <i>W</i> is a position-dependent matrix-valued potential satisfying certain smoothness condition in the angular variable. A consequence of our results are upper bounds for the growth in time of the expected size of the system and its total angular momentum.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 5","pages":"1821 - 1864"},"PeriodicalIF":1.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216777","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}
引用次数: 0
Aharonov–Casher Theorems for Dirac Operators on Manifolds with Boundary and APS Boundary Condition 有边界和 APS 边界条件的流形上狄拉克算子的阿哈诺夫-卡舍尔定理
IF 1.55 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-09-05 DOI: 10.1007/s00023-024-01482-7
M. Fialová
{"title":"Aharonov–Casher Theorems for Dirac Operators on Manifolds with Boundary and APS Boundary Condition","authors":"M. Fialová","doi":"10.1007/s00023-024-01482-7","DOIUrl":"https://doi.org/10.1007/s00023-024-01482-7","url":null,"abstract":"<p>The Aharonov–Casher theorem is a result on the number of the so-called zero modes of a system described by the magnetic Pauli operator in <span>(mathbb {R}^2)</span>. In this paper we address the same question for the Dirac operator on a flat two-dimensional manifold with boundary and Atiyah–Patodi–Singer boundary condition. More concretely we are interested in the plane and a disc with a finite number of circular holes cut out. We consider a smooth compactly supported magnetic field on the manifold and an arbitrary magnetic field inside the holes.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"59 1","pages":""},"PeriodicalIF":1.55,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216778","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}
引用次数: 0
Undressing the Electron 脱掉电子衣服
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-09-04 DOI: 10.1007/s00023-024-01476-5
Andrzej Herdegen
{"title":"Undressing the Electron","authors":"Andrzej Herdegen","doi":"10.1007/s00023-024-01476-5","DOIUrl":"10.1007/s00023-024-01476-5","url":null,"abstract":"<div><p>The extended algebra of the free electromagnetic fields, including infrared-singular fields, and the almost radial gauge, both introduced earlier, are postulated for the construction of the quantum electrodynamics in a Hilbert space (no indefinite metric). Both the Dirac and electromagnetic fields are constructed up to the first order (based on the incoming fields) as operators in the Hilbert space and shown to have physically well-interpretable asymptotic behavior in far past and spacelike separations. The Dirac field tends in far past to the free incoming field, carrying its own Coulomb field, but with no ‘soft photon dressing.’ The spacelike asymptotic limit of the electromagnetic field yields a conserved operator field, which is a sum of contributions of the incoming Coulomb field, and of the low-energy limit of the incoming free electromagnetic field. This should agree with the operator field similarly constructed with the use of outgoing fields, which then relates these past and future characteristics. Higher orders are expected not to change this picture, but their construction needs a treatment of the UV question, which has not been undertaken and remains a problem for further investigation.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 4","pages":"1443 - 1476"},"PeriodicalIF":1.4,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01476-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216788","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}
引用次数: 0
Classical Dynamical r-matrices for the Chern–Simons Formulation of Generalized 3d Gravity 广义三维引力的切尔-西蒙斯公式的经典动力学 r 矩阵
IF 1.55 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-09-03 DOI: 10.1007/s00023-024-01477-4
Juan Carlos Morales Parra, Bernd J. Schroers
{"title":"Classical Dynamical r-matrices for the Chern–Simons Formulation of Generalized 3d Gravity","authors":"Juan Carlos Morales Parra, Bernd J. Schroers","doi":"10.1007/s00023-024-01477-4","DOIUrl":"https://doi.org/10.1007/s00023-024-01477-4","url":null,"abstract":"<p>Classical dynamical <i>r</i>-matrices arise naturally in the combinatorial description of the phase space of Chern–Simons theories, either through the inclusion of dynamical sources or through a gauge fixing procedure involving two punctures. Here we consider classical dynamical <i>r</i>-matrices for the family of Lie algebras which arise in the Chern–Simons formulation of 3d gravity, for any value of the cosmological constant. We derive differential equations for classical dynamical <i>r</i>-matrices in this case and show that they can be viewed as generalized complexifications, in a sense which we define, of the equations governing dynamical <i>r</i>-matrices for <span>(mathfrak {su}(2))</span> and <span>(mathfrak {sl}(2,{mathbb {R}}))</span>. We obtain explicit families of solutions and relate them, via Weierstrass factorization, to solutions found by Feher, Gabor, Marshall, Palla and Pusztai in the context of chiral WZWN models.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"34 1","pages":""},"PeriodicalIF":1.55,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216806","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}
引用次数: 0
Anisotropic Ising Model in (d+s) Dimensions 各向异性等效模型在 $$d+s$$ 维度上的应用
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-08-27 DOI: 10.1007/s00023-024-01475-6
Estevão F. Borel, Aldo Procacci, Rémy Sanchis, Roger W. C. Silva
{"title":"Anisotropic Ising Model in (d+s) Dimensions","authors":"Estevão F. Borel,&nbsp;Aldo Procacci,&nbsp;Rémy Sanchis,&nbsp;Roger W. C. Silva","doi":"10.1007/s00023-024-01475-6","DOIUrl":"10.1007/s00023-024-01475-6","url":null,"abstract":"<div><p>In this note, we consider the asymmetric nearest neighbor ferromagnetic Ising model on the <span>((d+s))</span>-dimensional unit cubic lattice <span>({mathbb {Z}}^{d+s})</span>, at inverse temperature <span>(beta =1)</span> and with coupling constants <span>(J_s&gt;0)</span> and <span>(J_d&gt;0)</span> for edges of <span>({mathbb {Z}}^s)</span> and <span>({mathbb {Z}}^d)</span>, respectively. We obtain a lower bound for the critical curve in the phase diagram of <span>((J_s,J_d))</span>. In particular, as <span>(J_d)</span> approaches its critical value from below, our result is directly related to the so-called dimensional crossover phenomenon.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 4","pages":"1519 - 1532"},"PeriodicalIF":1.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216780","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}
引用次数: 0
Graph Hörmander Systems 霍尔曼德系统图
IF 1.55 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-08-17 DOI: 10.1007/s00023-024-01474-7
Haojian Li, Marius Junge, Nicholas LaRacuente
{"title":"Graph Hörmander Systems","authors":"Haojian Li, Marius Junge, Nicholas LaRacuente","doi":"10.1007/s00023-024-01474-7","DOIUrl":"https://doi.org/10.1007/s00023-024-01474-7","url":null,"abstract":"<p>This paper extends the Bakry-Émery criterion relating the Ricci curvature and logarithmic Sobolev inequalities to the noncommutative setting. We obtain easily computable complete modified logarithmic Sobolev inequalities of graph Laplacians and Lindblad operators of the corresponding graph Hörmander systems. We develop the anti-transference principle stating that the matrix-valued modified logarithmic Sobolev inequalities of sub-Laplacian operators on a compact Lie group are equivalent to such inequalities of a family of the transferred Lindblad operators with a uniform lower bound.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"29 1","pages":""},"PeriodicalIF":1.55,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216783","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}
引用次数: 0
The Sobolev Wavefront Set of the Causal Propagator in Finite Regularity 有限正则因果传播者的索波列夫波前集
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-27 DOI: 10.1007/s00023-024-01462-x
Yafet E. Sanchez Sanchez, Elmar Schrohe
{"title":"The Sobolev Wavefront Set of the Causal Propagator in Finite Regularity","authors":"Yafet E. Sanchez Sanchez,&nbsp;Elmar Schrohe","doi":"10.1007/s00023-024-01462-x","DOIUrl":"10.1007/s00023-024-01462-x","url":null,"abstract":"<div><p>Given a globally hyperbolic spacetime <span>(M={mathbb {R}}times Sigma )</span> of dimension four and regularity <span>(C^tau )</span>, we estimate the Sobolev wavefront set of the causal propagator <span>(K_G)</span> of the Klein–Gordon operator. In the smooth case, the propagator satisfies <span>(WF'(K_G)=C)</span>, where <span>(Csubset T^*(Mtimes M))</span> consists of those points <span>((tilde{x},tilde{xi },tilde{y},tilde{eta }))</span> such that <span>(tilde{xi },tilde{eta })</span> are cotangent to a null geodesic <span>(gamma )</span> at <span>(tilde{x})</span> resp. <span>(tilde{y})</span> and parallel transports of each other along <span>(gamma )</span>. We show that for <span>(tau &gt;2)</span>, </p><div><div><span>$$begin{aligned} WF'^{-2+tau -{epsilon }}(K_G)subset C end{aligned}$$</span></div></div><p>for every <span>({epsilon }&gt;0)</span>. Furthermore, in regularity <span>(C^{tau +2})</span> with <span>(tau &gt;2)</span>, </p><div><div><span>$$begin{aligned} Csubset WF'^{-frac{1}{2}}(K_G)subset WF'^{tau -epsilon }(K_G)subset C end{aligned}$$</span></div></div><p>holds for <span>(0&lt;epsilon &lt;tau +frac{1}{2})</span>. In the ultrastatic case with <span>(Sigma )</span> compact, we show <span>(WF'^{-frac{3}{2}+tau -epsilon }(K_G)subset C)</span> for <span>(epsilon &gt;0)</span> and <span>(tau &gt;2)</span> and <span>(WF'^{-frac{3}{2}+tau -epsilon }(K_G)= C)</span> for <span>(tau &gt;3)</span> and <span>(epsilon &lt;tau -3)</span>. Moreover, we show that the global regularity of the propagator <span>(K_G)</span> is <span>(H^{-frac{1}{2}-epsilon }_{loc}(Mtimes M))</span> as in the smooth case.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 4","pages":"1375 - 1406"},"PeriodicalIF":1.4,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01462-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141774520","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}
引用次数: 0
Correction to: ‘On Multimatrix Models Motivated by Random Noncommutative Geometry II: A Yang-Mills-Higgs Matrix Model’ Correction to：论随机非交换几何激励的多矩阵模型 II：杨-米尔斯-希格斯矩阵模型
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-18 DOI: 10.1007/s00023-024-01456-9
Carlos I. Perez-Sanchez
{"title":"Correction to: ‘On Multimatrix Models Motivated by Random Noncommutative Geometry II: A Yang-Mills-Higgs Matrix Model’","authors":"Carlos I. Perez-Sanchez","doi":"10.1007/s00023-024-01456-9","DOIUrl":"10.1007/s00023-024-01456-9","url":null,"abstract":"","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 2","pages":"757 - 758"},"PeriodicalIF":1.4,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01456-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141826232","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}
引用次数: 0
Discrete Symplectic Fermions on Double Dimers and Their Virasoro Representation 双二聚体上的离散辛费米子及其Virasoro表示
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-17 DOI: 10.1007/s00023-024-01455-w
David Adame-Carrillo
{"title":"Discrete Symplectic Fermions on Double Dimers and Their Virasoro Representation","authors":"David Adame-Carrillo","doi":"10.1007/s00023-024-01455-w","DOIUrl":"10.1007/s00023-024-01455-w","url":null,"abstract":"<div><p>A discrete version of the conformal field theory of symplectic fermions is introduced and discussed. Specifically, discrete symplectic fermions are realised as holomorphic observables in the double-dimer model. Using techniques of discrete complex analysis, the space of local fields of discrete symplectic fermions on the square lattice is proven to carry a representation of the Virasoro algebra with central charge <span>(-2)</span>.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 3","pages":"845 - 876"},"PeriodicalIF":1.4,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01455-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726657","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}
引用次数: 0
Sharp Semiclassical Spectral Asymptotics for Local Magnetic Schrödinger Operators on ({mathbb {R}}^d) Without Full Regularity 没有完全正则性的$${mathbb {R}}^d$$ 上局部磁薛定谔算子的尖锐半经典谱渐近学
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-16 DOI: 10.1007/s00023-024-01471-w
Søren Mikkelsen
{"title":"Sharp Semiclassical Spectral Asymptotics for Local Magnetic Schrödinger Operators on ({mathbb {R}}^d) Without Full Regularity","authors":"Søren Mikkelsen","doi":"10.1007/s00023-024-01471-w","DOIUrl":"10.1007/s00023-024-01471-w","url":null,"abstract":"<div><p>We consider operators acting in <span>(L^2({mathbb {R}}^d))</span> with <span>(dge 3)</span> that locally behave as a magnetic Schrödinger operator. For the magnetic Schrödinger operators, we suppose the magnetic potentials are smooth and the electric potential is five times differentiable and the fifth derivatives are Hölder continuous. Under these assumptions, we establish sharp spectral asymptotics for localised counting functions and Riesz means.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 5","pages":"1865 - 1906"},"PeriodicalIF":1.4,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01471-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141640932","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}
引用次数: 0
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