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Elliptic Solutions of the Toda Lattice with Constraint of Type B and Deformed Ruijsenaars–Schneider System 带约束的B型和变形rujsenaars - schneider系统Toda格的椭圆解
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-08-03 DOI: 10.1007/s11040-023-09462-9
V. Prokofev, A. Zabrodin
{"title":"Elliptic Solutions of the Toda Lattice with Constraint of Type B and Deformed Ruijsenaars–Schneider System","authors":"V. Prokofev,&nbsp;A. Zabrodin","doi":"10.1007/s11040-023-09462-9","DOIUrl":"10.1007/s11040-023-09462-9","url":null,"abstract":"<div><p>We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars–Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By studying more general elliptic solutions (elliptic families), we also suggest an extension of the deformed Ruijsenaars–Schneider system to a field theory.\u0000</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45235756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Discrete Field Theory: Symmetries and Conservation Laws 离散场论：对称性与守恒定律
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-08-03 DOI: 10.1007/s11040-023-09459-4
M. Skopenkov
{"title":"Discrete Field Theory: Symmetries and Conservation Laws","authors":"M. Skopenkov","doi":"10.1007/s11040-023-09459-4","DOIUrl":"10.1007/s11040-023-09459-4","url":null,"abstract":"<div><p>We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any symmetry. This gives exact conservation laws for several theories, e.g., lattice electrodynamics and gauge theory. In particular, we construct a conserved discrete energy–momentum tensor, approximating the continuum one at least for free fields. The theory is stated in topological terms, such as coboundary and products of cochains.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46824337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Extensions and Generalizations of Lattice Gelfand–Dickey Hierarchy 晶格Gelfand-Dickey层次的扩展与推广
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-07-29 DOI: 10.1007/s11040-023-09461-w
Lixiang Zhang, Chuanzhong Li
{"title":"Extensions and Generalizations of Lattice Gelfand–Dickey Hierarchy","authors":"Lixiang Zhang,&nbsp;Chuanzhong Li","doi":"10.1007/s11040-023-09461-w","DOIUrl":"10.1007/s11040-023-09461-w","url":null,"abstract":"<div><p>In this paper, for the extended lattice Gelfand–Dickey hierarchy, we construct its <i>n</i>-fold Darboux transformation and additional flows. And we prove that these flows are actually symmetries of the extended lattice Gelfand–Dickey hierarchy. Further, we show how the additional flows act on the tau function. On this basis, we generalize the extended lattice Gelfand–Dickey hierarchy to the multicomponent and noncommutative versions, and give the Lax equations, Sato equations, zero-curvature equations and other equivalent expressions of these versions. Moreover, we investigate their Darboux transformations and additional symmetries.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43266335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Global Minimum of the Energy–Momentum Relation for the Polaron 极化子能量-动量关系的全局极小值
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-07-26 DOI: 10.1007/s11040-023-09460-x
Jonas Lampart, David Mitrouskas, Krzysztof Myśliwy
{"title":"On the Global Minimum of the Energy–Momentum Relation for the Polaron","authors":"Jonas Lampart,&nbsp;David Mitrouskas,&nbsp;Krzysztof Myśliwy","doi":"10.1007/s11040-023-09460-x","DOIUrl":"10.1007/s11040-023-09460-x","url":null,"abstract":"<div><p>For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-023-09460-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47232248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Existence and Uniqueness of Solutions to Backward 2D and 3D Stochastic Convective Brinkman–Forchheimer Equations Forced by Lévy Noise lsamvy噪声强迫下的倒向二维和三维随机对流Brinkman-Forchheimer方程解的存在唯一性
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-07-03 DOI: 10.1007/s11040-023-09458-5
Manil T. Mohan
{"title":"Existence and Uniqueness of Solutions to Backward 2D and 3D Stochastic Convective Brinkman–Forchheimer Equations Forced by Lévy Noise","authors":"Manil T. Mohan","doi":"10.1007/s11040-023-09458-5","DOIUrl":"10.1007/s11040-023-09458-5","url":null,"abstract":"<div><p>The two- and three-dimensional incompressible backward stochastic convective Brinkman–Forchheimer (BSCBF) equations on a torus driven by Lévy noise are considered in this paper. A-priori estimates for adapted solutions of the finite-dimensional approximation of 2D and 3D BSCBF equations are obtained. For a given terminal data, the existence and uniqueness of pathwise adapted strong solutions is proved by using a standard Galerkin (or spectral) approximation technique and exploiting the monotonicity arguments. We also establish the continuity of the adapted solutions with respect to the terminal data. The above results are obtained for the absorption exponent <span>(rin [1,infty ))</span> for <span>(d=2)</span> and <span>(rin [3,infty ))</span> for <span>(d=3)</span>, and any Brinkman coefficient <span>(mu &gt;0)</span>, Forchheimer coefficient <span>(beta &gt;0)</span>, and hence the 3D critical case (<span>(r=3)</span>) is also handled successfully. We deduce analogous results for 2D backward stochastic Navier–Stokes equations perturbed by Lévy noise also.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-023-09458-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4125172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Self-Adjointness of a Class of Multi-Spin–Boson Models with Ultraviolet Divergences 一类具有紫外发散的多自旋玻色子模型的自伴随性
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-06-12 DOI: 10.1007/s11040-023-09457-6
Davide Lonigro
{"title":"Self-Adjointness of a Class of Multi-Spin–Boson Models with Ultraviolet Divergences","authors":"Davide Lonigro","doi":"10.1007/s11040-023-09457-6","DOIUrl":"10.1007/s11040-023-09457-6","url":null,"abstract":"<div><p>We study a class of quantum Hamiltonian models describing a family of <i>N</i> two-level systems (spins) coupled with a structured boson field of positive mass, with a rotating-wave coupling mediated by form factors possibly exhibiting ultraviolet divergences. Spin–spin interactions which do not modify the total number of excitations are also included. Generalizing previous results in the single-spin case, we provide explicit expressions for the self-adjointness domain and the resolvent of these models, both of them carrying an intricate dependence on the spin–field and spin–spin coupling via a family of concatenated propagators. This construction is also shown to be stable, in the norm resolvent sense, under approximations of the form factors via normalizable ones, for example an ultraviolet cutoff.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-023-09457-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4801137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On Quantum Optimal Transport 关于量子最优输运
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-06-06 DOI: 10.1007/s11040-023-09456-7
Sam Cole, Michał Eckstein, Shmuel Friedland, Karol Życzkowski
{"title":"On Quantum Optimal Transport","authors":"Sam Cole,&nbsp;Michał Eckstein,&nbsp;Shmuel Friedland,&nbsp;Karol Życzkowski","doi":"10.1007/s11040-023-09456-7","DOIUrl":"10.1007/s11040-023-09456-7","url":null,"abstract":"<div><p>We analyze a quantum version of the Monge–Kantorovich optimal transport problem. The quantum transport cost related to a Hermitian cost matrix <i>C</i> is minimized over the set of all bipartite coupling states <span>(rho ^{AB})</span> with fixed reduced density matrices <span>(rho ^A)</span> and <span>(rho ^B)</span> of size <i>m</i> and <i>n</i>. The minimum quantum optimal transport cost <span>(textrm{T}^Q_{C}(rho ^A,rho ^B))</span> can be efficiently computed using semidefinite programming. In the case <span>(m=n)</span> the cost <span>(textrm{T}^Q_{C})</span> gives a semidistance if and only if <i>C</i> is positive semidefinite and vanishes exactly on the subspace of symmetric matrices. Furthermore, if <i>C</i> satisfies the above conditions, then <span>(sqrt{textrm{T}^Q_{C}})</span> induces a quantum analogue of the Wasserstein-2 distance. Taking the quantum cost matrix <span>(C^Q)</span> to be the projector on the antisymmetric subspace, we provide a semi-analytic expression for <span>(textrm{T}^Q_{C^Q})</span> for any pair of single-qubit states and show that its square root yields a transport distance on the Bloch ball. Numerical simulations suggest that this property holds also in higher dimensions. Assuming that the cost matrix suffers decoherence and that the density matrices become diagonal, we study the quantum-to-classical transition of the Monge–Kantorovich distance, propose a continuous family of interpolating distances, and demonstrate that the quantum transport is cheaper than the classical one. Furthermore, we introduce a related quantity—the SWAP-fidelity—and compare its properties with the standard Uhlmann–Jozsa fidelity. We also discuss the quantum optimal transport for general <i>d</i>-partite systems.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-023-09456-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4259382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Braided Hopf Algebras and Gauge Transformations II: (*)-Structures and Examples 编织Hopf代数和规范变换II: (*) -结构和例子
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-05-11 DOI: 10.1007/s11040-023-09454-9
Paolo Aschieri, Giovanni Landi, Chiara Pagani
{"title":"Braided Hopf Algebras and Gauge Transformations II: (*)-Structures and Examples","authors":"Paolo Aschieri,&nbsp;Giovanni Landi,&nbsp;Chiara Pagani","doi":"10.1007/s11040-023-09454-9","DOIUrl":"10.1007/s11040-023-09454-9","url":null,"abstract":"<div><p>We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebras of infinitesimal gauge transformations of bundles on noncommutative spheres. The braiding of these algebras is implemented by the triangular structure of the symmetry Hopf algebra. We present a systematic analysis of compatible <span>(*)</span>-structures, encompassing the quasitriangular case.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-023-09454-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4474601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Consistency of the Bäcklund Transformation for the Spin Calogero–Moser System 自旋卡罗热-莫泽体系Bäcklund变换的一致性
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-05-08 DOI: 10.1007/s11040-023-09450-z
Bjorn K. Berntson
{"title":"Consistency of the Bäcklund Transformation for the Spin Calogero–Moser System","authors":"Bjorn K. Berntson","doi":"10.1007/s11040-023-09450-z","DOIUrl":"10.1007/s11040-023-09450-z","url":null,"abstract":"<div><p>We prove the consistency of the Bäcklund transformation (BT) for the spin Calogero–Moser (sCM) system in the rational, trigonometric, and hyperbolic cases. The BT for the sCM system consists of an overdetermined system of ordinary differential equations; to establish our result, we construct and analyze certain functions that measure the departure of this overdetermined system from consistency. We show that these functions are identically zero and that this allows for a unique solution to the initial value problem for the overdetermined system.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-023-09450-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4353637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Hydrodynamical Behavior for the Symmetric Simple Partial Exclusion with Open Boundary 开边界对称简单部分不相容的流体力学行为
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-05-08 DOI: 10.1007/s11040-023-09446-9
C. Franceschini, P. Gonçalves, B. Salvador
{"title":"Hydrodynamical Behavior for the Symmetric Simple Partial Exclusion with Open Boundary","authors":"C. Franceschini,&nbsp;P. Gonçalves,&nbsp;B. Salvador","doi":"10.1007/s11040-023-09446-9","DOIUrl":"10.1007/s11040-023-09446-9","url":null,"abstract":"<div><p>We analyze the symmetric simple partial exclusion process, which allows at most <span>(alpha )</span> particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter <span>(theta in {mathbb {R}})</span>. We prove that the hydrodynamic behavior is given by the heat equation and depending on the value of <span>(theta )</span>, the equation is supplemented with different boundary conditions. Setting <span>(alpha = 1)</span> we find the results known in Baldasso et al. (J Stat Phys 167(5):1112–1142, 2017) and Bernardin et al. (Markov Processes Relat. Fields 25:217–274, 2017) for the symmetric simple exclusion process.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4350497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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