Reports on Mathematical Physics最新文献

{"title":"Spirality kernel ideal flows","authors":"Artin Khaleghi,&nbsp;Helia Farahbakhsh,&nbsp;Mobin Wesari,&nbsp;Mohsen Hazrati,&nbsp;Homayoon Eshraghi","doi":"10.1016/S0034-4877(26)00066-2","DOIUrl":"10.1016/S0034-4877(26)00066-2","url":null,"abstract":"<div><div>Understanding the formation of singularities in ideal fluid flows remains one of the most challenging problems in mathematical fluid dynamics. While analytical and numerical approaches have been widely studied, topological aspects of vortex dynamics are less explored. In this work, we investigate a topological and Lagrangian invariant called spirality, whose vanishing may facilitate singularity formation in ideal flows. We define a special class of flows-spirality kernel flows-for which the spirality vanishes identically. We show that these flows are preserved under smooth, boundary-preserving diffeomorphisms of the initial domain, giving rise to a rich homotopy-theoretic structure. This includes the definition of equivalence classes, groupoid actions, and chains of spirality kernel flows, potentially leading to a classification scheme for such flows. We also discuss possible generalizations to higher-dimensional manifolds and discrete cochain settings. These results suggest a novel topological framework that could offer new insights into the geometric origins of vortex singularities.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"98 2","pages":"Pages 199-206"},"PeriodicalIF":1.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149257823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Riemann solitons on four-dimensional nilpotent Lie groups","authors":"Jinguo Jiang,&nbsp;Yanni Yang","doi":"10.1016/S0034-4877(26)00064-9","DOIUrl":"10.1016/S0034-4877(26)00064-9","url":null,"abstract":"<div><div>This paper presents a complete classification of Riemann solitons on all left-invariant Lorentzian metrics of the four-dimensional nilpotent Lie groups\u0000\t\t\t\t<span><math><msub><mi>H</mi><mrow><mn>3</mn></mrow></msub><mo>×</mo><mrow><mi>R</mi></mrow></math></span> and <em>G</em>₄. By solving the Riemann soliton equation explicitly for each metric family, we find solutions for the families\u0000\t\t\t\t<span><math><msub><mi>g</mi><mrow><mi>U</mi></mrow></msub></math></span> (covering\u0000\t\t\t\t<span><math><msub><mi>g</mi><mrow><mi>μ</mi></mrow></msub></math></span> and\u0000\t\t\t\t<span><math><msubsup><mi>g</mi><mrow><mi>λ</mi></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>) and <em>g</em>₁ on\u0000\t\t\t\t<span><math><msub><mi>H</mi><mrow><mn>3</mn></mrow></msub><mo>×</mo><mrow><mi>R</mi></mrow></math></span>, but prove that none exist for <em>g</em>₃. On <em>G</em>₄, no left-invariant Lorentzian metric admits a Riemann soliton. This shows that, for the metric families considered in this paper, the Riemann soliton condition is more restrictive than the Ricci soliton condition.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"98 2","pages":"Pages 169-188"},"PeriodicalIF":1.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149257824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Constructing generalized hypergeometric coherent states by diagonal ordering operation technique","authors":"Messan Médard Akouetegan,&nbsp;Isiaka Aremua,&nbsp;Mahouton Norbert Hounkonnou","doi":"10.1016/S0034-4877(26)00068-6","DOIUrl":"10.1016/S0034-4877(26)00068-6","url":null,"abstract":"<div><div>This work deals with the diagonal ordering operation technique (DOOT) applied to generate generalized hypergeometric coherent states for special functions (GHCSs-SF), and to generalized photon added hypergeometric coherent states (GPAH-CSs). For every set of coherent states, the density operator for mixed (thermal) states is formulated with its <em>P</em>-representation provided from the DOOT method, and the associated mathematical and physical properties are analyzed. In addition, the thermodynamic properties are studied from the expression of the density operator obtained for each representation of the corresponding class of coherent states.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"98 2","pages":"Pages 221-245"},"PeriodicalIF":1.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149257974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Ricci flows perturbation and fluctuations of the charge-current density in 2D string black hole models","authors":"Jun Yan","doi":"10.1016/S0034-4877(26)00069-8","DOIUrl":"10.1016/S0034-4877(26)00069-8","url":null,"abstract":"<div><div>The perturbation equation for the Ricci flows in two-dimensional string σ model is studied in this article, it can be derived from the Gauss-Codazzi equations, and it has been used to obtain the perturbation solutions in two black hole models. In the dilaton black hole model, the Hawking temperature and the temperature flow are given by the analytical solution of the perturbation equation. In addition, we get the asymptotic perturbation solution in the loop correction black hole model, the fluctuation flows for the charge-current density are derived according to the solutions of the perturbation Dirac equation. The evolution trend of the Hawking temperature flow and the fluctuation flows with the momentum scale are analyzed and discussed.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"98 2","pages":"Pages 247-260"},"PeriodicalIF":1.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149257975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Existence and uniqueness for a Schrödinger system via Nash equilibrium approach","authors":"B. Slimani,&nbsp;A. Ouahab,&nbsp;J.J. Nieto","doi":"10.1016/S0034-4877(26)00070-4","DOIUrl":"10.1016/S0034-4877(26)00070-4","url":null,"abstract":"<div><div>In this paper we prove the existence and uniqueness of a solution to a coupled nonlinear Schrödinger system with coercive potentials by characterizing it as a Nash-type equilibrium of the associated energy functionals. Using variational methods and a Perov-type fixed-point argument, we show that the solution operator is a contraction in\u0000\t\t\t\t<span><math><msup><mi>H</mi><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow><mo>×</mo><msup><mi>H</mi><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow></math></span>, under subcritical growth conditions on the nonlinearities.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"98 2","pages":"Pages 261-280"},"PeriodicalIF":1.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149257977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Generalized almost ω-Ricci solitons on relativistic bulk viscous fluid string spacetime","authors":"Shahroud Azami,&nbsp;Mehdi Jafari,&nbsp;Uday Chand De","doi":"10.1016/S0034-4877(26)00063-7","DOIUrl":"10.1016/S0034-4877(26)00063-7","url":null,"abstract":"<div><div>In this study, we analyze the behaviour of generalized almost ω-Ricci solitons and their gradient variants within the context of relativistic bulk viscous fluid string spacetime. The analysis starts by expressing the divergence of the vector field associated with these solitons, linking it explicitly to the scalar curvature characteristic of the considered spacetime model. Using the soliton framework as a geometric tool, we establish key conditions that the scalar curvature must satisfy. Furthermore, criteria delineating when the soliton exhibits contraction, equilibrium, or expansion phases are rigorously formulated.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"98 2","pages":"Pages 149-168"},"PeriodicalIF":1.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149257822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"On a class of time-dependent non-hermitian hamiltonians","authors":"F. Kecita,&nbsp;B. Khantoul,&nbsp;A. Bounames","doi":"10.1016/S0034-4877(26)00067-4","DOIUrl":"10.1016/S0034-4877(26)00067-4","url":null,"abstract":"<div><div>We study a class of time-dependent (TD) non-Hermitian Hamiltonians\u0000\t\t\t\t<span><math><mi>H</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> that can be transformed into a time-independent pseudo-Hermitian Hamiltonian\u0000\t\t\t\t<span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mrow><mi>PH</mi></mrow></mrow></msubsup></math></span> using a suitable TD unitary transformation <em>F(t)</em>. The latter can in turn be related to a Hermitian Hamiltonian <em>h</em> by a similarity transformation\u0000\t\t\t\t<span><math><mrow><mi>h</mi><mo>=</mo><mi>ρ</mi><msubsup><mi>Η</mi><mn>0</mn><mrow><mi>P</mi><mi>H</mi></mrow></msubsup><msup><mi>ρ</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></math></span>, where ρ is the Dyson map. Accordingly, once the Schrödinger equation for the Hermitian Hamiltonian <em>h</em> is solved, the general solution of the initial system can be deduced. This allows to define the appropriate\u0000\t\t\t\t<span><math><mover><mi>η</mi><mo>˜</mo></mover></math></span>(<em>t</em>)-inner product for the Hilbert space associated with <em>H(t)</em>, where\u0000\t\t\t\t<span><math><mrow><mover><mi>η</mi><mo>~</mo></mover></mrow><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><msup><mi>F</mi><mrow><mo>†</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mi>η</mi><mi>F</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> and\u0000\t\t\t\t<span><math><mi>η</mi><mo>=</mo><msup><mi>ρ</mi><mrow><mo>†</mo></mrow></msup><mi>ρ</mi></math></span> is the metric operator. This greatly simplifies the computation of the relevant uncertainty relations for these systems. As an example, we consider a model of a particle with a TD mass subjected to a specific TD complex linear potential. We thus obtain two Hermitian Hamiltonians, namely that of the standard harmonic oscillator and that of the inverted oscillator. For both cases, the auxiliary equation admits a solution, and the exact analytical solutions are given in terms of the Hermite polynomials with complex coefficients. Moreover, when the Hermitian Hamiltonian is that of the harmonic oscillator, the position-momentum uncertainty relation is real and greater than or equal to\u0000\t\t\t\t<span><math><mrow><mi>ℏ</mi><mo>/</mo><mn>2</mn></mrow></math></span>, thereby confirming its consistency.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"98 2","pages":"Pages 207-219"},"PeriodicalIF":1.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149257976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"On orthoposets of numerical events in quantum logic","authors":"Dietmar Dorninger,&nbsp;Helmut Länger","doi":"10.1016/S0034-4877(26)00065-0","DOIUrl":"10.1016/S0034-4877(26)00065-0","url":null,"abstract":"<div><div>Let <em>S</em> be a set of states of a physical system and <em>p</em>(<em>s</em>) the probability of the occurrence of an event when the system is in state <em>s</em> ∈ <em>S</em>. Such a function <em>p</em>: <em>S</em> → [0, 1] is known as a numerical event or more accurately an <em>S</em>-probability. A set <em>P</em> of numerical events including the constant functions 0 and 1 and the value 1 − <em>p</em> with every <em>p</em> ∈ <em>P</em> becomes a poset when ordered by the order of real functions and can serve as a general setting for quantum logics. We call such a poset <em>P</em> a general set of events (GSE). The thoroughly investigated algebras of <em>S</em>-probabilities (including Hilbert logics), concrete logics and Boolean algebras can all be represented within this setting. In this paper we study various classes of GSEs, in particular those that are orthoposets and their interrelations and connections to known logics. Moreover, we characterize GSEs as posets by means of states and discuss the situation for GSEs to be lattices.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"98 2","pages":"Pages 189-197"},"PeriodicalIF":1.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149257973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Resurgence theory and holomorphic quantum mechanics","authors":"M.W. AlMasri","doi":"10.1016/S0034-4877(26)00062-5","DOIUrl":"10.1016/S0034-4877(26)00062-5","url":null,"abstract":"<div><div>In this work, we study the resurgence program in holomorphic quantum mechanics. As a specific problem, we investigate the resurgence in the quartic anharmonic oscillator within holomorphic quantum mechanics, using the Bargmann representation of bosonic operators. In this framework, the perturbative energy series is shown to be Gevrey-1 and Borel summable only after continuation across the Stokes line. The instanton operator, realized as a coherent-state displacement in the Segal-Bargmann space, provides an explicit operatorial bridge between perturbative coefficients and nonperturbative sectors. Alien derivative relations generate the full resurgence triangle characteristic of the Bender-Wu model, and the resummed energy is expressed as a trans-series via a ratio of expectation values involving this instanton operator. As a concrete demonstration, we compute the first seven energy levels <em>(n=0, …, 6)</em> up to sixth order in the coupling <em>g</em>; the resulting exact rational coefficients reproduce the classic Bender-Wu results, confirming the consistency and power of the holomorphic resurgence approach.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"98 2","pages":"Pages 131-148"},"PeriodicalIF":1.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149257821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"On Virtual Displacements of Material Systems with Nonholonomic Constraints","authors":"Alexander Sumbatov","doi":"10.1016/S0034-4877(26)00052-2","DOIUrl":"10.1016/S0034-4877(26)00052-2","url":null,"abstract":"<div><div>In analytical mechanics of systems with ideal nonholonomic constraints, the question of the existence of constraints described by nonlinear in velocities equations remains unresolved. The few known examples of such constraints are usually constructed, as a rule, artificially, using auxiliary subsystems involving massless rigid rods, threads, and other devices whose mechanical motion is neglected. This paper analyses several published but incorrect examples of nonlinear nonholonomic constraints. Conversely, constraints of the second kind (servo constraints) are not ideal, may be described by rather complex nonlinear equations, and are realized using energy sources external to the system. Irrespective of the condition of ideality of constraints, there exists a most general definition of virtual displacements for constraints that are linear in accelerations. In certain cases, it is possible to derive a closed system of equations of motion without resorting to the expression for the virtual work of external forces. The article considers an example of such a system, related to the problem of stabilizing the upper equilibrium position of a movable rigid rod.</div></div><div>In analytical mechanics of systems with ideal nonholonomic constraints, the question of the existence of constraints described by nonlinear in velocities equations remains unresolved. The few known examples of such constraints are usually constructed, as a rule, artificially, using auxiliary subsystems involving massless rigid rods, threads, and other devices whose mechanical motion is neglected. This paper analyses several published but incorrect examples of nonlinear nonholonomic constraints. Conversely, constraints of the second kind (servo constraints) are not ideal, may be described by rather complex nonlinear equations, and are realized using energy sources external to the system. Irrespective of the condition of ideality of constraints, there exists a most general definition of virtual displacements for constraints that are linear in accelerations. In certain cases, it is possible to derive a closed system of equations of motion without resorting to the expression for the virtual work of external forces. The article considers an example of such a system, related to the problem of stabilizing the upper equilibrium position of a movable rigid rod.</div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"98 1","pages":"Pages 29-42"},"PeriodicalIF":1.0,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148964854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}