Communications in Mathematical Physics最新文献_第9页

Characterization of k-Positive Maps k-正映射的表征

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05250-4

Tomasz Młynik, Hiroyuki Osaka, Marcin Marciniak

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On a Variational Problem Related to the Cwikel–Lieb–Rozenblum and Lieb–Thirring Inequalities 关于Cwikel-Lieb-Rozenblum和Lieb-Thirring不等式的一个变分问题

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-07 DOI: 10.1007/s00220-024-05216-y

Thiago Carvalho Corso, Tobias Ried

{"title":"On a Variational Problem Related to the Cwikel–Lieb–Rozenblum and Lieb–Thirring Inequalities","authors":"Thiago Carvalho Corso, Tobias Ried","doi":"10.1007/s00220-024-05216-y","DOIUrl":"10.1007/s00220-024-05216-y","url":null,"abstract":"<div>We explicitly solve a variational problem related to upper bounds on the optimal constants in the Cwikel–Lieb–Rozenblum (CLR) and Lieb–Thirring (LT) inequalities, which has recently been derived in Hundertmark et al. (Invent Math 231:111–167, 2023. https://doi.org/10.1007/s00222-022-01144-7) and Frank et al. (Eur Math Soc 23(8):2583–2600, 2021. https://doi.org/10.1090/pspum/104/01877). We achieve this through a variational characterization of the (L^1) norm of the Fourier transform of a function and duality, from which we obtain a reformulation in terms of a variant of the Hadamard three lines lemma. By studying Hardy-like spaces of holomorphic functions in a strip in the complex plane, we are able to provide an analytic formula for the minimizers, and use it to get the best possible upper bounds for the optimal constants in the CLR and LT inequalities achievable by the method of Hundertmark et al. (Invent Math 231:111–167, 2023. https://doi.org/10.1007/s00222-022-01144-7) and Frank et al. (Eur Math Soc 23(8):2583–2600, 2021. https://doi.org/10.1090/pspum/104/01877).</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05216-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Crystallization of (hbox {C}^*)-Algebras (hbox {C}^*) -代数的结晶

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-06 DOI: 10.1007/s00220-024-05212-2

Marcelo Laca, Sergey Neshveyev, Makoto Yamashita

{"title":"Crystallization of (hbox {C}^*)-Algebras","authors":"Marcelo Laca, Sergey Neshveyev, Makoto Yamashita","doi":"10.1007/s00220-024-05212-2","DOIUrl":"10.1007/s00220-024-05212-2","url":null,"abstract":"<div>Given a (hbox {C}^*)-algebra A with an almost periodic time evolution (sigma ), we define a new (hbox {C}^*)-algebra (A_c), which we call the crystal of ((A,sigma )), that represents the zero temperature limit of ((A, sigma )). We prove that there is a one-to-one correspondence between the ground states of ((A,sigma )) and the states on (A_c), justifying the name. In order to investigate further the relation between low temperature equilibrium states on A and traces on (A_c), we define a Fock module (mathcal {F}) over the crystal and construct a vacuum representation of A on (mathcal {F}). This allows us to show, under relatively mild assumptions, that for sufficiently large inverse temperatures (beta ) the (sigma )-(hbox {KMS}_beta )-states on A are induced from traces on (A_c) by means of the Fock module. In the second part, we compare the K-theoretic structures of A and (A_c). Previous work by various authors suggests that they have (rationally) isomorphic K-groups. We analyze this phenomenon in detail, confirming it under favorable conditions, but showing that, in general, there is apparently no easy way to relate these groups. As examples, we discuss in particular Exel’s results on semi-saturated circle actions, and recent results of Miller on the K-theory of inverse semigroup (hbox {C}^*)-algebras. In relation to the latter, we introduce the notion of a scale N on an inverse semigroup I and define a new inverse semigroup (I_c), which we call the crystal of (I, N).</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05212-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 Tail Distribution of the Partition Function for Directed Polymers in the Weak Disorder Phase 定向聚合物弱无序相配分函数的尾部分布

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-05 DOI: 10.1007/s00220-025-05246-0

Stefan Junk, Hubert Lacoin

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Truncated Affine Rozansky–Witten Models as Extended Defect TQFTs 截断仿射Rozansky-Witten模型作为扩展缺陷tqft

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-01-28 DOI: 10.1007/s00220-024-05164-7

Ilka Brunner, Nils Carqueville, Pantelis Fragkos, Daniel Roggenkamp

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Determination of Stable Branches of Relative Equilibria of the N-Vortex Problem on the Sphere 球面上n -涡旋问题相对平衡态稳定分支的确定

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-01-28 DOI: 10.1007/s00220-024-05220-2

K. Constantineau, C. García-Azpeitia, L. C. García-Naranjo, J.-P. Lessard

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Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms 紧支微分同态群的广义正能量表示

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-01-28 DOI: 10.1007/s00220-024-05226-w

Bas Janssens, Milan Niestijl

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Regularity of Conjugacies of Linearizable Generalized Interval Exchange Transformations 可线性广义区间交换变换共轭的正则性

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-01-18 DOI: 10.1007/s00220-024-05197-y

Selim Ghazouani, Corinna Ulcigrai

{"title":"Regularity of Conjugacies of Linearizable Generalized Interval Exchange Transformations","authors":"Selim Ghazouani, Corinna Ulcigrai","doi":"10.1007/s00220-024-05197-y","DOIUrl":"10.1007/s00220-024-05197-y","url":null,"abstract":"<div>We consider generalized interval exchange transformations (GIETs) of (dge 2) intervals which are linearizable, i.e. differentiably conjugated to standard interval exchange maps (IETs) via a diffeomorphism h of [0, 1] and study the regularity of the conjugacy h. Using a renormalization operator obtained accelerating Rauzy–Veech induction, we show that, under a full measure condition on the IET obtained by linearization, if the orbit of the GIET under renormalization converges exponentially fast in a ({mathcal {C}}^2) distance to the subspace of IETs, there exists an exponent (0<alpha <1) such that h is ({mathcal {C}}^{1+alpha }). Combined with the results proved by the authors in [4], this implies in particular the following improvement of the rigidity result in genus two proved in [4] (from ({mathcal {C}}^1) to ({mathcal {C}}^{1+alpha }) rigidity): for almost every irreducible IET (T_0 ) with (d=4) or (d=5), for any GIET which is topologically conjugate to (T_0) via a homeomorphism h and has vanishing boundary, the topological conjugacy h is actually a ({mathcal {C}}^{1+alpha }) diffeomorphism, i.e. a diffeomorphism h with derivative Dh which is (alpha )-Hölder continuous.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05197-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

From Decay of Correlations to Locality and Stability of the Gibbs State 从相关衰减到吉布斯态的局域性和稳定性

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-01-18 DOI: 10.1007/s00220-024-05198-x

Ángela Capel, Massimo Moscolari, Stefan Teufel, Tom Wessel

{"title":"From Decay of Correlations to Locality and Stability of the Gibbs State","authors":"Ángela Capel, Massimo Moscolari, Stefan Teufel, Tom Wessel","doi":"10.1007/s00220-024-05198-x","DOIUrl":"10.1007/s00220-024-05198-x","url":null,"abstract":"<div>We show that whenever the Gibbs state of a quantum spin system satisfies decay of correlations, then it is stable, in the sense that local perturbations affect the Gibbs state only locally, and it satisfies local indistinguishability, i.e. it exhibits local insensitivity to system size. These implications hold in any dimension, require only locality of the Hamiltonian, and are based on Lieb–Robinson bounds and on a detailed analysis of the locality properties of the quantum belief propagation for Gibbs states. To demonstrate the versatility of our approach, we explicitly apply our results to several physically relevant models in which the decay of correlations is either known to hold or is proved by us. These include Gibbs states of one-dimensional spin chains with polynomially decaying interactions at any temperature, and high-temperature Gibbs states of quantum spin systems with finite-range interactions in any dimension. We also prove exponential decay of correlations above a threshold temperature for Gibbs states of one-dimensional finite spin chains with translation-invariant and exponentially decaying interactions, and then apply our general results.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05198-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 Modular Invariance of Quantum Affine W-Algebras 量子仿射w -代数的模不变性

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-01-18 DOI: 10.1007/s00220-024-05223-z

Victor G. Kac, Minoru Wakimoto

{"title":"On Modular Invariance of Quantum Affine W-Algebras","authors":"Victor G. Kac, Minoru Wakimoto","doi":"10.1007/s00220-024-05223-z","DOIUrl":"10.1007/s00220-024-05223-z","url":null,"abstract":"<div>We find modular transformations of normalized characters for the following W-algebras: (a) (W_k^{min}(mathfrak {g}), text {where } mathfrak {g}=D_n (nge 4), text {or } E_6, E_7, E_8,) and k is a negative integer (ge -2), or (ge -frac{h^vee }{6}-1), respectively; (b) quantum Hamiltonian reduction of the (hat{mathfrak {g}})-module (L(k Lambda _0)), where (mathfrak {g}) is a simple Lie algebra, f is its non-zero nilpotent element, and k is a principal admissible level with the denominator (u>theta (x)), where 2x is the Dynkin characteristic of f, and (theta ) is the highest root of (mathfrak {g}). We prove that these vertex algebras are modular invariant. A conformal vertex algebra V is called modular invariant if its character (tr_V q^{L_0-c/24}) converges to a holomorphic modular function in the complex upper half-plane on a congruence subgroup. We find explicit formulas for their characters. Modular invariance of V is important since, in particular, conjecturally it implies that V is simple, and that V is rational, provided that it is lisse.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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