发布求助
文献互助 智能选刊 最新文献

Annales Henri Poincaré最新文献

筛选
英文 中文
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 1.55 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, Mostafa Sabri","doi":"10.1007/s00023-024-01470-x","DOIUrl":"https://doi.org/10.1007/s00023-024-01470-x","url":null,"abstract":"<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>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"58 1","pages":""},"PeriodicalIF":1.55,"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
A Short Proof of Bose–Einstein Condensation in the Gross–Pitaevskii Regime and Beyond 玻色-爱因斯坦凝结在格罗斯-皮塔耶夫斯基及其他状态下的简短证明
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-01 DOI: 10.1007/s00023-024-01465-8
Christian Brennecke, Morris Brooks, Cristina Caraci, Jakob Oldenburg
{"title":"A Short Proof of Bose–Einstein Condensation in the Gross–Pitaevskii Regime and Beyond","authors":"Christian Brennecke,&nbsp;Morris Brooks,&nbsp;Cristina Caraci,&nbsp;Jakob Oldenburg","doi":"10.1007/s00023-024-01465-8","DOIUrl":"10.1007/s00023-024-01465-8","url":null,"abstract":"<div><p>We consider dilute Bose gases on the three-dimensional unit torus that interact through a pair potential with scattering length of order <span>( N^{kappa -1})</span>, for some <span>(kappa &gt;0)</span>. For the range <span>( kappa in [0, frac{1}{43}))</span>, Adhikari et al. (Ann Henri Poincaré 22:1163–1233, 2021) proves complete BEC of low energy states into the zero momentum mode based on a unitary renormalization through operator exponentials that are quartic in creation and annihilation operators. In this paper, we give a new and self-contained proof of BEC of the ground state for <span>( kappa in [0, frac{1}{20}))</span> by combining some of the key ideas of Adhikari et al. (Ann Henri Poincaré 22:1163–1233, 2021) with the novel diagonalization approach introduced recently in Brooks (Diagonalizing Bose Gases in the Gross–Pitaevskii Regime and Beyond, arXiv:2310.11347), which is based on the Schur complement formula. In particular, our proof avoids the use of operator exponentials and is significantly simpler than Adhikari et al. (Ann Henri Poincaré 22:1163–1233, 2021).</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 4","pages":"1353 - 1373"},"PeriodicalIF":1.4,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01465-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501765","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
Spectral Convergence of the Dirac Operator on Typical Hyperbolic Surfaces of High Genus 典型高属双曲面上狄拉克算子的谱收敛性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-01 DOI: 10.1007/s00023-024-01452-z
Laura Monk, Rareş Stan
{"title":"Spectral Convergence of the Dirac Operator on Typical Hyperbolic Surfaces of High Genus","authors":"Laura Monk,&nbsp;Rareş Stan","doi":"10.1007/s00023-024-01452-z","DOIUrl":"10.1007/s00023-024-01452-z","url":null,"abstract":"<div><p>In this article, we study the Dirac spectrum of typical hyperbolic surfaces of finite area, equipped with a nontrivial spin structure (so that the Dirac spectrum is discrete). For random Weil–Petersson surfaces of large genus <i>g</i> with <span>(o(sqrt{g}))</span> cusps, we prove convergence of the spectral density to the spectral density of the hyperbolic plane, with quantitative error estimates. This result implies upper bounds on spectral counting functions and multiplicities, as well as a uniform Weyl law, true for typical hyperbolic surfaces equipped with any nontrivial spin structure.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 1","pages":"365 - 387"},"PeriodicalIF":1.4,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01452-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532107","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
Time Functions on Lorentzian Length Spaces 洛伦兹长度空间上的时间函数
IF 1.55 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-07-01 DOI: 10.1007/s00023-024-01461-y
Annegret Burtscher, Leonardo García-Heveling
{"title":"Time Functions on Lorentzian Length Spaces","authors":"Annegret Burtscher, Leonardo García-Heveling","doi":"10.1007/s00023-024-01461-y","DOIUrl":"https://doi.org/10.1007/s00023-024-01461-y","url":null,"abstract":"<p>In general relativity, time functions are crucial objects whose existence and properties are intimately tied to the causal structure of a spacetime and also to the initial value formulation of the Einstein equations. In this work we establish all fundamental classical existence results on time functions in the setting of Lorentzian (pre-)length spaces (including causally plain continuous spacetimes, closed cone fields and even more singular spaces). More precisely, we characterize the existence of time functions by <i>K</i>-causality, show that a modified notion of Geroch’s volume functions are time functions if and only if the space is causally continuous, and lastly, characterize global hyperbolicity by the existence of Cauchy time functions, and Cauchy sets. Our results thus inevitably show that no manifold structure is needed in order to obtain suitable time functions.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"33 1","pages":""},"PeriodicalIF":1.55,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532111","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信