{"title":"Higher order polynomial complex invariants for one-dimensional anharmonic potentials","authors":"S.B. Bhardwaj, Ram Mehar Singh, Vipin Kumar, Narender Kumar, Fakir Chand, Shalini Gupta","doi":"10.1016/S0034-4877(24)00011-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00011-9","url":null,"abstract":"<div><p>Exact quadratic in momenta complex invariants are investigated for both time independent and time dependent one-dimensional Hamiltonian systems possessing higher order nonlinearities within the framework of the rationalization method. The extended complex phase space approach is utilized to map a real system into complex space. Such invariants are expected to play a role in the analysis of complex trajectories and help to understand some new phenomena associated with complex potentials.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000119/pdfft?md5=7de74f018141c5f672b53eea0e7fe658&pid=1-s2.0-S0034487724000119-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}
Giuseppe Dattoli, Mariano Carpanese, Emanuele Di Palma, Alberto Petralia
{"title":"A note on the magnetic multipole polynomials","authors":"Giuseppe Dattoli, Mariano Carpanese, Emanuele Di Palma, Alberto Petralia","doi":"10.1016/S0034-4877(24)00014-4","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00014-4","url":null,"abstract":"<div><p>A family of two variable polynomials naturally emerges from the expansion in multipoles of a magnetic field. The order of the expansion fixes the polynomial degree and the multipolar content: dipole, quadrupole, sextupole and so on. The associated polynomials share analogies with Hermite-type families. The relevant properties are studied, within an umbral framework, which simplifies the derivation of the associated mathematical technicalities. We take advantage from this analogy to present a fairly general discussion about the properties of the “magnetic” polynomials. We touch on the possibility of embedding the results of the present study in a dedicated algorithm for the analysis of the transport of a charged beam in a magnetic structure.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000144/pdfft?md5=e7262f46398b4f88b7e6034a078ff7ac&pid=1-s2.0-S0034487724000144-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}
Afzal Raghavi, Ramazan Ali Mohammadian, Saeed Mohammadi
{"title":"A unified approach to the generalized uncertainty principle","authors":"Afzal Raghavi, Ramazan Ali Mohammadian, Saeed Mohammadi","doi":"10.1016/S0034-4877(24)00010-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00010-7","url":null,"abstract":"<div><p>In this work, some of the present scenarios for the generalized uncertainty principle are reviewed and it is shown that all of them could be derived through a unified approach that guarantees the existence of both, minimal measurable length and maximal available momentum. Then, a new proposal is introduced that compensates for the defects of previous models. We also studied the effects of this modification on the energy levels and the wave function of a simple harmonic oscillator. It is shown that for the case of a harmonic oscillator, generalized uncertainty relation results in an uncertainty relation between the frequency and the mass of the oscillator.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000107/pdfft?md5=ec5294c0bc792165889cdbcb39cd59a6&pid=1-s2.0-S0034487724000107-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}
Bang-Yen Chen, Mohammed Jamali, Mohammad Hasan Shahid
{"title":"Solitons on multiply warped product manifolds","authors":"Bang-Yen Chen, Mohammed Jamali, Mohammad Hasan Shahid","doi":"10.1016/S0034-4877(24)00013-2","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00013-2","url":null,"abstract":"<div><p>In this paper, we study different solitons on multiply warped product manifolds and realize the geometry of base manifold and fiber manifolds. We also study the base manifolds and fiber manifolds when the multiply warped product manifold is either concircularly flat or conharmonically flat.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000132/pdfft?md5=bc6c15830310ff8cf8c726be658e7fe2&pid=1-s2.0-S0034487724000132-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}
{"title":"On Construction of Darboux integrable discrete models","authors":"Kostyantyn Zheltukhin, Natalya Zheltukhina","doi":"10.1016/s0034-4877(23)00080-0","DOIUrl":"https://doi.org/10.1016/s0034-4877(23)00080-0","url":null,"abstract":"<p>The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the continuous equation. In the present paper, the discretization of the differential-discrete equations is done using the corresponding characteristic algebras. New examples of integrable discrete equations are obtained.</p>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061683","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}
Maciej Błaszak, Błażej M. Szablikowski, Krzysztof Marciniak
{"title":"Stäckel representations of stationary Kdv systems","authors":"Maciej Błaszak, Błażej M. Szablikowski, Krzysztof Marciniak","doi":"10.1016/s0034-4877(23)00083-6","DOIUrl":"https://doi.org/10.1016/s0034-4877(23)00083-6","url":null,"abstract":"<p>In this article we study Stäckel representations of stationary KdV systems<span>. Using Lax formalism we prove that these systems have two different representations as separable Stäckel systems of Benenti type, related with different foliations of the stationary manifold. We do it by constructing an explicit transformation between the jet coordinates of stationary KdV systems and separation variables of the corresponding Benenti systems for arbitrary number of degrees of freedom. Moreover, on the stationary manifold, we present the explicit form of Miura map between both representations of stationary KdV systems, which also yields their bi-Hamiltonian formulation.</span></p>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139062826","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":"Magnetic Neumann Laplacian on a domain with a hole","authors":"Diana Barseghyan, Baruch Schneider, Swanhild Bernstein","doi":"10.1016/s0034-4877(23)00079-4","DOIUrl":"https://doi.org/10.1016/s0034-4877(23)00079-4","url":null,"abstract":"<p>In this article, we study the magnetic Neumann Laplacian on a domain with a small hole. Our attention is focused on the description of holes, which do not change the spectrum drastically. Moreover, we show that the spectrum of the magnetic Neumann Laplacian converges in the sense of the Hausdorff distance to the spectrum of the original operator defined on the unperturbed domain.</p>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061629","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":"Nonequilibrium thermodynamics as a symplecto-contact reduction and relative information entropy","authors":"Jin-wook Lim, Yong-Geun Oh","doi":"10.1016/s0034-4877(23)00084-8","DOIUrl":"https://doi.org/10.1016/s0034-4877(23)00084-8","url":null,"abstract":"<p>Both statistical phase space (SPS), which is Γ = <em>T</em>* <span><math><mrow is=\"true\"><mi is=\"true\" mathvariant=\"double-struck\">R</mi></mrow></math></span><sup>3<em>N</em></sup> of <em>N</em><span><span>-body particle system, and kinetic theory phase space (KTPS), which is the </span>cotangent bundle </span><em>T</em>* <span><math><mrow is=\"true\"><mi is=\"true\" mathvariant=\"double-struck\">P</mi></mrow></math></span>(Γ) of the probability space <span><math><mrow is=\"true\"><mi is=\"true\" mathvariant=\"double-struck\">P</mi></mrow></math></span><span><span><span>(Γ) thereon, carry canonical symplectic structures. Starting from this first principle<span>, we provide a canonical derivation of thermodynamic phase space (TPS) of nonequilibrium thermodynamics as a </span></span>contact manifold<span><span> in two steps. First, regarding the collective observation of observables in SPS as a moment map defined on KTPS, we apply the Marsden–Weinstein reduction and obtain a mesoscopic phase space in between KTPS and TPS as a (infinite-dimensional) symplectic fibration. Then we show that the reduced relative information entropy defines a generating function that provides a covariant construction of a </span>thermodynamic equilibrium as a Legen-drian </span></span>submanifold<span><span>. This Legendrian submanifold is not necessarily graph-like. We interpret the </span>Maxwell construction of </span></span><em>equal-area law</em><span> as the procedure of finding a continuous, not necessarily differentiable, thermodynamic potential<span> and explain the associated phase transition by identifying the procedure with that of finding a graph selector in symplecto-contact geometry and in the Aubry-Mather theory of dynamical system.</span></span></p>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061693","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":"A categorical view on the principle of relativity","authors":"L.M. Gaio, B.F. Rizzuti","doi":"10.1016/s0034-4877(23)00081-2","DOIUrl":"https://doi.org/10.1016/s0034-4877(23)00081-2","url":null,"abstract":"<p>Category theory<span> plays a special role in mathematics — it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this work, we present another application of category in physics, related to the principle of relativity. The operational construction of (inertial) frames of reference indicates that only the movement between one and another frame is enough to differentiate both of them. This fact is hidden when one applies only group theory to connect frames. In fact, rotations and translations only change coordinates, keeping the frame inert. The change of frames is only attainable by boosts in the classical and relativistic regimes for both Galileo and Lorentz (Poincaré) groups. Besides providing a nontrivial example of application of category theory in physics, we also fulfill the presented gap when one directly applies group theory for connecting frames.</span></p>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061694","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":"Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees","authors":"N.N. Ganikhodjaev, N.M. Khatamov, U.A. Rozikov","doi":"10.1016/s0034-4877(23)00082-4","DOIUrl":"https://doi.org/10.1016/s0034-4877(23)00082-4","url":null,"abstract":"<p><span>The work is devoted to gradient Gibbs measures (GGMs) of an SOS model with countable set\u0000</span><span><math><mrow is=\"true\"><mi is=\"true\" mathvariant=\"double-struck\">Z</mi></mrow></math></span> of spin values and having alternating magnetism on Cayley trees. This model is defined by a nearest-neighbour gradient interaction potential. Using Külske-Schriever argument, based on boundary law equations, we give several <em>q</em>-height-periodic translations invariant GGMs for <em>q</em> = 2, 3, 4.</p>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139072304","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}
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