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Annales Henri Poincaré最新文献

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Painlevé Kernels and Surface Defects at Strong Coupling 强耦合下的潘列韦核与表面缺陷
IF 1.55 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-14 DOI: 10.1007/s00023-024-01469-4
Matijn François, Alba Grassi
{"title":"Painlevé Kernels and Surface Defects at Strong Coupling","authors":"Matijn François, Alba Grassi","doi":"10.1007/s00023-024-01469-4","DOIUrl":"https://doi.org/10.1007/s00023-024-01469-4","url":null,"abstract":"<p>It is well established that the spectral analysis of canonically quantized four-dimensional Seiberg–Witten curves can be systematically studied via the Nekrasov–Shatashvili functions. In this paper, we explore another aspect of the relation between <span>({mathcal {N}}=2)</span> supersymmetric gauge theories in four dimensions and operator theory. Specifically, we study an example of an integral operator associated with Painlevé equations and whose spectral traces are related to correlation functions of the 2d Ising model. This operator does not correspond to a canonically quantized Seiberg–Witten curve, but its kernel can nevertheless be interpreted as the density matrix of an ideal Fermi gas. Adopting the approach of Tracy and Widom, we provide an explicit expression for its eigenfunctions via an <span>({{,mathrm{O(2)},}})</span> matrix model. We then show that these eigenfunctions are computed by surface defects in <span>({{,mathrm{SU(2)},}})</span> super Yang–Mills in the self-dual phase of the <span>(Omega )</span>-background. Our result also yields a strong coupling expression for such defects which resums the instanton expansion. Even though we focus on one concrete example, we expect these results to hold for a larger class of operators arising in the context of isomonodromic deformation equations.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"33 1","pages":""},"PeriodicalIF":1.55,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609037","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
Renormalization of Higher Currents of the Sine-Gordon Model in pAQFT pAQFT 中辛-戈登模型高次电流的重正化
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-12 DOI: 10.1007/s00023-024-01468-5
Fabrizio Zanello
{"title":"Renormalization of Higher Currents of the Sine-Gordon Model in pAQFT","authors":"Fabrizio Zanello","doi":"10.1007/s00023-024-01468-5","DOIUrl":"10.1007/s00023-024-01468-5","url":null,"abstract":"<div><p>In this paper, we show that the higher currents of the sine-Gordon model are super-renormalizable by power counting in the framework of pAQFT. First we obtain closed recursive formulas for the higher currents in the classical theory and introduce a suitable notion of degree for their components. We then move to the pAQFT setting, and by means of some technical results, we compute explicit formulas for the unrenormalized interacting currents. Finally, we perform what we call the piecewise renormalization of the interacting higher currents, showing that the renormalization process involves a number of steps which is bounded by the degree of the classical conserved currents.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 4","pages":"1407 - 1442"},"PeriodicalIF":1.4,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01468-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609039","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
On Lieb–Robinson Bounds for a Class of Continuum Fermions 关于一类连续费米子的列布-罗宾逊边界
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-12 DOI: 10.1007/s00023-024-01453-y
Benjamin Hinrichs, Marius Lemm, Oliver Siebert
{"title":"On Lieb–Robinson Bounds for a Class of Continuum Fermions","authors":"Benjamin Hinrichs,&nbsp;Marius Lemm,&nbsp;Oliver Siebert","doi":"10.1007/s00023-024-01453-y","DOIUrl":"10.1007/s00023-024-01453-y","url":null,"abstract":"<div><p>We consider the quantum dynamics of a many-fermion system in <span>({{mathbb {R}}}^d)</span> with an ultraviolet regularized pair interaction as previously studied in Gebert et al. (Ann Henri Poincaré 21(11):3609–3637, 2020). We provide a Lieb–Robinson bound under substantially relaxed assumptions on the potentials. We also improve the associated one-body Lieb–Robinson bound on <span>(L^2)</span>-overlaps to an almost ballistic one (i.e., an almost linear light cone) under the same relaxed assumptions. Applications include the existence of the infinite-volume dynamics and clustering of ground states in the presence of a spectral gap. We also develop a fermionic continuum notion of conditional expectation and use it to approximate time-evolved fermionic observables by local ones, which opens the door to other applications of the Lieb–Robinson bounds.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 1","pages":"41 - 80"},"PeriodicalIF":1.4,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01453-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609038","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
3D Tensor Renormalisation Group at High Temperatures 高温下的三维张量重正化群
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-09 DOI: 10.1007/s00023-024-01464-9
Nikolay Ebel
{"title":"3D Tensor Renormalisation Group at High Temperatures","authors":"Nikolay Ebel","doi":"10.1007/s00023-024-01464-9","DOIUrl":"10.1007/s00023-024-01464-9","url":null,"abstract":"<div><p>Building upon previous 2D studies, this research focuses on describing 3D tensor renormalisation group (RG) flows for lattice spin systems, such as the Ising model. We present a novel RG map, which operates on tensors with infinite-dimensional legs and does not involve truncations, in contrast to numerical tensor RG maps. To construct this map, we developed new techniques for analysing tensor networks. Our analysis shows that the constructed RG map contracts the region around the tensor <span>(A_*)</span>, corresponding to the high-temperature phase of the 3D Ising model. This leads to the iterated RG map convergence in the Hilbert–Schmidt norm to <span>(A_*)</span> when initialised in the vicinity of <span>(A_*)</span>. This work provides the first steps towards the rigorous understanding of tensor RG maps in 3D.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 4","pages":"1291 - 1351"},"PeriodicalIF":1.4,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574943","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
Ergodic Theorems for Continuous-Time Quantum Walks on Crystal Lattices and the Torus 晶体网格和环上连续时间量子行走的遍历定理
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-08 DOI: 10.1007/s00023-024-01470-x
Anne Boutet de Monvel, Mostafa Sabri
{"title":"Ergodic Theorems for Continuous-Time Quantum Walks on Crystal Lattices and the Torus","authors":"Anne Boutet de Monvel,&nbsp;Mostafa Sabri","doi":"10.1007/s00023-024-01470-x","DOIUrl":"10.1007/s00023-024-01470-x","url":null,"abstract":"<div><p>We give several quantum dynamical analogs of the classical Kronecker–Weyl theorem, which says that the trajectory of free motion on the torus along almost every direction tends to equidistribute. As a quantum analog, we study the quantum walk <span>(exp (-textrm{i}t Delta ) psi )</span> starting from a localized initial state <span>(psi )</span>. Then, the flow will be ergodic if this evolved state becomes equidistributed as time goes on. We prove that this is indeed the case for evolutions on the flat torus, provided we start from a point mass, and we prove discrete analogs of this result for crystal lattices. On some periodic graphs, the mass spreads out non-uniformly, on others it stays localized. Finally, we give examples of quantum evolutions on the sphere which do not equidistribute.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 5","pages":"1733 - 1767"},"PeriodicalIF":1.4,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574945","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
Deviation of Top Eigenvalue for Some Tridiagonal Matrices Under Various Moment Assumptions 不同矩假设下某些三对角矩阵的顶特征值偏差
IF 1.55 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-06 DOI: 10.1007/s00023-024-01467-6
Yi Han
{"title":"Deviation of Top Eigenvalue for Some Tridiagonal Matrices Under Various Moment Assumptions","authors":"Yi Han","doi":"10.1007/s00023-024-01467-6","DOIUrl":"https://doi.org/10.1007/s00023-024-01467-6","url":null,"abstract":"<p>Symmetric tridiagonal matrices appear ubiquitously in mathematical physics, serving as the matrix representation of discrete random Schrödinger operators. In this work, we investigate the top eigenvalue of these matrices in the large deviation regime, assuming the random potentials are on the diagonal with a certain decaying factor <span>(N^{-{alpha }})</span>, and the probability law <span>(mu )</span> of the potentials satisfies specific decay assumptions. We investigate two different models, one of which has random matrix behavior at the spectral edge but the other does not. Both the light-tailed regime, i.e., when <span>(mu )</span> has all moments, and the heavy-tailed regime are covered. Precise right tail estimates and a crude left tail estimate are derived. In particular, we show that when the tail <span>(mu )</span> has a certain decay rate, then the top eigenvalue is distributed as the Fréchet law composed with some deterministic functions. The proof relies on computing one-point perturbations of fixed tridiagonal matrices.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"48 1","pages":""},"PeriodicalIF":1.55,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574944","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
Canonical Typicality for Other Ensembles than Micro-canonical 微观典型性之外的其他组合的典型性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-02 DOI: 10.1007/s00023-024-01466-7
Stefan Teufel, Roderich Tumulka, Cornelia Vogel
{"title":"Canonical Typicality for Other Ensembles than Micro-canonical","authors":"Stefan Teufel,&nbsp;Roderich Tumulka,&nbsp;Cornelia Vogel","doi":"10.1007/s00023-024-01466-7","DOIUrl":"10.1007/s00023-024-01466-7","url":null,"abstract":"<div><p>We generalize Lévy’s lemma, a concentration-of-measure result for the uniform probability distribution on high-dimensional spheres, to a much more general class of measures, so-called GAP measures. For any given density matrix <span>(rho )</span> on a separable Hilbert space <span>({mathcal {H}})</span>, <span>({textrm{GAP}}(rho ))</span> is the most spread-out probability measure on the unit sphere of <span>({mathcal {H}})</span> that has density matrix <span>(rho )</span> and thus forms the natural generalization of the uniform distribution. We prove concentration-of-measure whenever the largest eigenvalue <span>(Vert rho Vert )</span> of <span>(rho )</span> is small. We use this fact to generalize and improve well-known and important typicality results of quantum statistical mechanics to GAP measures, namely canonical typicality and dynamical typicality. Canonical typicality is the statement that for “most” pure states <span>(psi )</span> of a given ensemble, the reduced density matrix of a sufficiently small subsystem is very close to a <span>(psi )</span>-independent matrix. Dynamical typicality is the statement that for any observable and any unitary time evolution, for “most” pure states <span>(psi )</span> from a given ensemble the (coarse-grained) Born distribution of that observable in the time-evolved state <span>(psi _t)</span> is very close to a <span>(psi )</span>-independent distribution. So far, canonical typicality and dynamical typicality were known for the uniform distribution on finite-dimensional spheres, corresponding to the micro-canonical ensemble, and for rather special mean-value ensembles. Our result shows that these typicality results hold also for <span>({textrm{GAP}}(rho ))</span>, provided the density matrix <span>(rho )</span> has small eigenvalues. Since certain GAP measures are quantum analogs of the canonical ensemble of classical mechanics, our results can also be regarded as a version of equivalence of ensembles.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 4","pages":"1477 - 1518"},"PeriodicalIF":1.4,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01466-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532110","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
The Double Semion State in Infinite Volume 无限体积中的双半子状态
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-02 DOI: 10.1007/s00023-024-01445-y
Alex Bols, Boris Kjær, Alvin Moon
{"title":"The Double Semion State in Infinite Volume","authors":"Alex Bols,&nbsp;Boris Kjær,&nbsp;Alvin Moon","doi":"10.1007/s00023-024-01445-y","DOIUrl":"10.1007/s00023-024-01445-y","url":null,"abstract":"<div><p>We describe in a simple setting how to extract a braided tensor category from a collection of superselection sectors of a two-dimensional quantum spin system, corresponding to abelian anyons. We extract from this category its fusion ring as well as its F and R-symbols. We then construct the double semion state in infinite volume and extract the braided tensor category describing its semion, anti-semion, and bound state excitations. We verify that this category is equivalent to the representation category of the twisted quantum double <span>(mathcal {D}^{phi }(mathbb {Z}_2))</span>.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 3","pages":"1009 - 1053"},"PeriodicalIF":1.4,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01445-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532108","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
Large Deviations for the Ground State of Weakly Interacting Bose Gases 弱相互作用玻色气体基态的大偏差
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-02 DOI: 10.1007/s00023-024-01463-w
Simone Rademacher
{"title":"Large Deviations for the Ground State of Weakly Interacting Bose Gases","authors":"Simone Rademacher","doi":"10.1007/s00023-024-01463-w","DOIUrl":"10.1007/s00023-024-01463-w","url":null,"abstract":"<div><p>We consider the ground state of a Bose gas of <i>N</i> particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose–Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas’ ground state correspond to dependent random variables due to the bosons’ correlation. We prove that in the limit <span>(N rightarrow infty )</span> bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 4","pages":"1239 - 1289"},"PeriodicalIF":1.4,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01463-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532112","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
Almost Optimal Upper Bound for the Ground State Energy of a Dilute Fermi Gas via Cluster Expansion 通过簇扩展实现稀费米气体基态能量的近乎最佳上限
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-02 DOI: 10.1007/s00023-024-01450-1
Asbjørn Bækgaard Lauritsen
{"title":"Almost Optimal Upper Bound for the Ground State Energy of a Dilute Fermi Gas via Cluster Expansion","authors":"Asbjørn Bækgaard Lauritsen","doi":"10.1007/s00023-024-01450-1","DOIUrl":"10.1007/s00023-024-01450-1","url":null,"abstract":"<div><p>We prove an upper bound on the energy density of the dilute spin-<span>(frac{1}{2})</span> Fermi gas capturing the leading correction to the kinetic energy <span>(8pi a rho _uparrow rho _downarrow )</span> with an error of size smaller than <span>(arho ^{2}(a^3rho )^{1/3-varepsilon })</span> for any <span>(varepsilon &gt; 0)</span>, where <i>a</i> denotes the scattering length of the interaction. The result is valid for a large class of interactions including interactions with a hard core. A central ingredient in the proof is a rigorous version of a fermionic cluster expansion adapted from the formal expansion of Gaudin et al. (Nucl Phys A 176(2):237–260, 1971. https://doi.org/10.1016/0375-9474(71)90267-3).</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 1","pages":"203 - 243"},"PeriodicalIF":1.4,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01450-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532109","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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