Communications in Mathematical Physics最新文献

Some Rigorous Results on the Lévy Spin Glass Model

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-27 DOI: 10.1007/s00220-025-05244-2

Wei-Kuo Chen, Heejune Kim, Arnab Sen

{"title":"Some Rigorous Results on the Lévy Spin Glass Model","authors":"Wei-Kuo Chen, Heejune Kim, Arnab Sen","doi":"10.1007/s00220-025-05244-2","DOIUrl":"10.1007/s00220-025-05244-2","url":null,"abstract":"<div><p>We study the Lévy spin glass model, a fully connected model on <i>N</i> vertices with heavy-tailed interactions governed by a power law distribution of order <span>(0<alpha <2.)</span> Our investigation is divided into three cases <span>(0<alpha <1)</span>, <span>(alpha =1)</span>, and <span>(1<alpha <2.)</span> When <span>(1<alpha <2,)</span> we identify a high temperature regime, in which the limit and fluctuation of the free energy are explicitly obtained and the site and bond overlaps are shown to exhibit concentration, interestingly, while the former is concentrated around zero, the latter obeys a positivity behavior. At any temperature, we further establish the existence of the limiting free energy and derive a variational formula analogous to Panchenko’s framework in the setting of the Poissonian Viana-Bray model. For <span>(alpha =1)</span>, the free energy scales super-linearly and converges to a constant proportional to <span>(beta )</span> in probability at any temperature. In the case of <span>(0<alpha <1)</span>, the scaling for the free energy is again super-linear, however, it converges weakly to the sum of a Poisson Point Process at any temperature. Additionally, we show that the Gibbs measure puts most of its mass on the configurations that align with signs of the polynomially many heaviest edge weights.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513206","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

Local Statistics and Concentration for Non-intersecting Brownian Bridges with Smooth Boundary Data

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-27 DOI: 10.1007/s00220-025-05251-3

Amol Aggarwal, Jiaoyang Huang

引用次数: 0

Twisted Verlinde Formula for Vertex Operator Algebras: The Prime Case 顶点算子代数的扭曲韦林德公式：质点案例

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-27 DOI: 10.1007/s00220-025-05248-y

Chongying Dong, Xingjun Lin

引用次数: 0

Efficient Quantum Gibbs Samplers with Kubo–Martin–Schwinger Detailed Balance Condition

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-27 DOI: 10.1007/s00220-025-05235-3

Zhiyan Ding, Bowen Li, Lin Lin

{"title":"Efficient Quantum Gibbs Samplers with Kubo–Martin–Schwinger Detailed Balance Condition","authors":"Zhiyan Ding, Bowen Li, Lin Lin","doi":"10.1007/s00220-025-05235-3","DOIUrl":"10.1007/s00220-025-05235-3","url":null,"abstract":"<div><p>Lindblad dynamics and other open-system dynamics provide a promising path towards efficient Gibbs sampling on quantum computers. In these proposals, the Lindbladian is obtained via an algorithmic construction akin to designing an artificial thermostat in classical Monte Carlo or molecular dynamics methods, rather than being treated as an approximation to weakly coupled system-bath unitary dynamics. Recently, Chen, Kastoryano, and Gilyén (arXiv:2311.09207) introduced the first efficiently implementable Lindbladian satisfying the Kubo–Martin–Schwinger (KMS) detailed balance condition, which ensures that the Gibbs state is a fixed point of the dynamics and is applicable to non-commuting Hamiltonians. This Gibbs sampler uses a continuously parameterized set of jump operators, and the energy resolution required for implementing each jump operator depends only logarithmically on the precision and the mixing time. In this work, we build upon the structural characterization of KMS detailed balanced Lindbladians by Fagnola and Umanità, and develop a family of efficient quantum Gibbs samplers using a finite set of jump operators (the number can be as few as one), akin to the classical Markov chain-based sampling algorithm. Compared to the existing works, our quantum Gibbs samplers have a comparable quantum simulation cost but with greater design flexibility and a much simpler implementation and error analysis. Moreover, it encompasses the construction of Chen, Kastoryano, and Gilyén as a special instance.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05235-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513397","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

Fiber 2-Functors and Tambara–Yamagami Fusion 2-Categories

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-20 DOI: 10.1007/s00220-025-05249-x

Thibault D. Décoppet, Matthew Yu

引用次数: 0

Large Amplitude Quasi-Periodic Traveling Waves in Two Dimensional Forced Rotating Fluids

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-20 DOI: 10.1007/s00220-025-05247-z

Roberta Bianchini, Luca Franzoi, Riccardo Montalto, Shulamit Terracina

引用次数: 0

Clustering Theorem in 1D Long-Range Interacting Systems at Arbitrary Temperatures

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-20 DOI: 10.1007/s00220-025-05242-4

Yusuke Kimura, Tomotaka Kuwahara

{"title":"Clustering Theorem in 1D Long-Range Interacting Systems at Arbitrary Temperatures","authors":"Yusuke Kimura, Tomotaka Kuwahara","doi":"10.1007/s00220-025-05242-4","DOIUrl":"10.1007/s00220-025-05242-4","url":null,"abstract":"<div><p>This paper delves into a fundamental aspect of quantum statistical mechanics—the absence of thermal phase transitions in one-dimensional (1D) systems. Originating from Ising’s analysis of the 1D spin chain, this concept has been pivotal in understanding 1D quantum phases, especially those with finite-range interactions, as extended by Araki. In this work, we focus on quantum long-range interactions and successfully derive a clustering theorem applicable to a wide range of interaction decays at arbitrary temperatures. This theorem applies to any interaction forms that decay faster than <span>(r^{-2})</span> and does not rely on translation invariance or infinite system size assumptions. Also, we rigorously established that the temperature dependence of the correlation length is given by <span>(e^{mathrm{const.} beta })</span>, which is the same as the classical cases. Our findings indicate the absence of phase transitions in 1D systems with super-polynomially decaying interactions, thereby expanding upon previous theoretical research. To overcome significant technical challenges originating from the divergence of the imaginary-time Lieb–Robinson bound, we utilize the quantum belief propagation to refine the cluster expansion method. This approach allowed us to address divergence issues effectively and contributed to a deeper understanding of low-temperature behaviors in 1D quantum systems.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05242-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455412","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

Quantum Langevin Dynamics for Optimization

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05234-4

Zherui Chen, Yuchen Lu, Hao Wang, Yizhou Liu, Tongyang Li

{"title":"Quantum Langevin Dynamics for Optimization","authors":"Zherui Chen, Yuchen Lu, Hao Wang, Yizhou Liu, Tongyang Li","doi":"10.1007/s00220-025-05234-4","DOIUrl":"10.1007/s00220-025-05234-4","url":null,"abstract":"<div><p>We initiate the study of utilizing quantum Langevin dynamics (QLD) to solve optimization problems, particularly those nonconvex objective functions that present substantial obstacles for traditional gradient descent algorithms. Specifically, we examine the dynamics of a system coupled with an infinite heat bath. This interaction induces both random quantum noise and a deterministic damping effect to the system, which nudge the system towards a steady state that hovers near the global minimum of objective functions. We theoretically prove the convergence of QLD in convex landscapes, demonstrating that the average energy of the system can converge to zero in the low temperature limit with an exponential convergence rate. Numerically, we first show the energy dissipation capability of QLD by retracing its origins to spontaneous emission. Furthermore, we conduct detailed discussion of the impact of each parameter. Finally, based on the observations when comparing QLD with the classical Fokker-Plank-Smoluchowski equation, we propose a time-dependent QLD by setting temperature and <span>(hbar )</span> as time-dependent parameters, which can be theoretically proven to converge better than the time-independent case and also outperforms a series of state-of-the-art quantum and classical optimization algorithms in many nonconvex landscapes.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430951","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

Spectral Bounds on Hyperbolic 3-Manifolds: Associativity and the Trace Formula

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-024-05222-0

James Bonifacio, Dalimil Mazáč, Sridip Pal

{"title":"Spectral Bounds on Hyperbolic 3-Manifolds: Associativity and the Trace Formula","authors":"James Bonifacio, Dalimil Mazáč, Sridip Pal","doi":"10.1007/s00220-024-05222-0","DOIUrl":"10.1007/s00220-024-05222-0","url":null,"abstract":"<div><p>We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds and orbifolds in three dimensions, including the standard Laplace--Beltrami operator on functions and the Laplacian on powers of the cotangent bundle. Our approach employs linear programming techniques to derive rigorous bounds by leveraging two types of spectral identities. The first type, inspired by the conformal bootstrap, arises from the consistency of the spectral decomposition of the product of Laplace eigensections, and involves the Laplacian spectra as well as integrals of triple products of eigensections. We formulate these conditions in the language of representation theory of <span>(textrm{PSL}_2(mathbb {C}))</span> and use them to prove upper bounds on the first and second Laplacian eigenvalues. The second type of spectral identities follows from the Selberg trace formula. We use them to find upper bounds on the spectral gap of the Laplace--Beltrami operator on hyperbolic 3-orbifolds, as well as on the systole length of hyperbolic 3-manifolds, as a function of the volume. Further, we prove that the spectral gap <span>(lambda _1)</span> of the Laplace--Beltrami operator on all closed hyperbolic 3-manifolds satisfies <span>(lambda _1 < 47.32)</span>. Along the way, we use the trace formula to estimate the low-energy spectra of a large set of example orbifolds and compare them with our general bounds, finding that the bounds are nearly sharp in several cases.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05222-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430985","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

New Variants of Arithmetic Quantum Ergodicity

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-024-05203-3

Peter Humphries, Jesse Thorner

引用次数: 0