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Galilean and Carrollian Hodge star operators 伽利略和卡罗尔霍奇星算子
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00007-7
Marián Fecko
{"title":"Galilean and Carrollian Hodge star operators","authors":"Marián Fecko","doi":"10.1016/S0034-4877(24)00007-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00007-7","url":null,"abstract":"<div><p>The standard Hodge star operator is naturally associated with metric tensor (and orientation). It is routinely used to concisely write down physics equations on, say, Lorentzian spacetimes. On Galilean (Carrollian) spacetimes, there is no canonical (nonsingular) metric tensor available. So, the usual construction of the Hodge star does not work. Here we propose analogs of the Hodge star operator on Galilean (Carrollian) spacetimes. They may be used to write down important physics equations, e.g. equations of Galilean (Carrollian) electrodynamics.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 1-19"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000077/pdfft?md5=95dc18d8cfd864d5e9758bc25b1ea4dd&pid=1-s2.0-S0034487724000077-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139975998","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}
引用次数: 0
Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems 交折射、余折射、接触和共接触哈密顿系统的四元数的列积分性
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00009-0
R. Azuaje
{"title":"Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems","authors":"R. Azuaje","doi":"10.1016/S0034-4877(24)00009-0","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00009-0","url":null,"abstract":"<div><p>In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We show that having a solvable Lie algebra of constants of motion for a Hamiltonian system is equivalent to having a solvable Lie algebra of symmetries of the vector field defining the dynamics of the system, which allows us to find solutions of the equations of motion by quadratures.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 37-56"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000090/pdfft?md5=c065113fa688f685b26c838f8320fc3d&pid=1-s2.0-S0034487724000090-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976000","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}
引用次数: 0
Zero-error correctibility and phase retrievability for twirling channels 旋转信道的零误差可纠正性和相位可检索性
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00012-0
Deguang Han, Kai Liu
{"title":"Zero-error correctibility and phase retrievability for twirling channels","authors":"Deguang Han,&nbsp;Kai Liu","doi":"10.1016/S0034-4877(24)00012-0","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00012-0","url":null,"abstract":"<div><p>A twirling channel is a quantum channel induced by a continuous unitary representation\u0000<span><math><mrow><mi>π</mi><mo>=</mo><msubsup><mo>∑</mo><mi>i</mi><mo>⊕</mo></msubsup><mrow><msub><mi>m</mi><mi>i</mi></msub><msub><mi>π</mi><mi>i</mi></msub></mrow></mrow></math></span> on a compact group <em>G</em>, where π<sub><em>i</em></sub> are inequivalent irreducible representations. Motivated by a recent work [<span>8</span>] on minimal mixed unitary rank of Φ<em><sub>π</sub></em>, we explore the connections of the independence number, zero-error capacity, quantum codes, orthogonality index and phase retrievability of the quantum channel Φ<em><sub>π</sub></em> with the irreducible representation multiplicities <em>m<sub>i</sub></em> and the irreducible representation dimensions dim\u0000<span><math><mrow><msub><mi>H</mi><mrow><msub><mi>π</mi><mi>i</mi></msub></mrow></msub></mrow></math></span>. In particular, we show that the independence number of Φ<em><sub>π</sub></em> is the sum of the multiplicities, the orthogonal index of Φ<em><sub>π</sub></em> is exactly the sum of those representation dimensions, and the zero-error capacity is equal to log\u0000<span><math><mrow><mrow><mo>(</mo><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></msubsup><mrow><msub><mi>m</mi><mi>i</mi></msub></mrow></mrow><mo>)</mo></mrow></mrow></math></span>. We also present a lower bound for the phase retrievability in terms of the minimal length of phase retrievable frames for ℂ<sup><em>n</em></sup></p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 87-102"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000120/pdfft?md5=c13c155f18d2d613dd2d69aa31d00367&pid=1-s2.0-S0034487724000120-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976004","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}
引用次数: 0
Higher order polynomial complex invariants for one-dimensional anharmonic potentials 一维非谐波势的高阶多项式复不变式
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00011-9
S.B. Bhardwaj, Ram Mehar Singh, Vipin Kumar, Narender Kumar, Fakir Chand, Shalini Gupta
{"title":"Higher order polynomial complex invariants for one-dimensional anharmonic potentials","authors":"S.B. Bhardwaj,&nbsp;Ram Mehar Singh,&nbsp;Vipin Kumar,&nbsp;Narender Kumar,&nbsp;Fakir Chand,&nbsp;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":"93 1","pages":"Pages 71-86"},"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}
引用次数: 0
A note on the magnetic multipole polynomials 关于磁多极多项式的说明
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00014-4
Giuseppe Dattoli, Mariano Carpanese, Emanuele Di Palma, Alberto Petralia
{"title":"A note on the magnetic multipole polynomials","authors":"Giuseppe Dattoli,&nbsp;Mariano Carpanese,&nbsp;Emanuele Di Palma,&nbsp;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":"93 1","pages":"Pages 121-127"},"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}
引用次数: 0
A unified approach to the generalized uncertainty principle 广义不确定性原理的统一方法
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00010-7
Afzal Raghavi, Ramazan Ali Mohammadian, Saeed Mohammadi
{"title":"A unified approach to the generalized uncertainty principle","authors":"Afzal Raghavi,&nbsp;Ramazan Ali Mohammadian,&nbsp;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":"93 1","pages":"Pages 57-69"},"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}
引用次数: 0
Solitons on multiply warped product manifolds 乘翘积流形上的孤子
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00013-2
Bang-Yen Chen, Mohammed Jamali, Mohammad Hasan Shahid
{"title":"Solitons on multiply warped product manifolds","authors":"Bang-Yen Chen,&nbsp;Mohammed Jamali,&nbsp;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":"93 1","pages":"Pages 103-119"},"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}
引用次数: 0
On Construction of Darboux integrable discrete models 论达尔布可积分离散模型的构建
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1016/S0034-4877(23)00080-0
Kostyantyn Zheltukhin, Natalya Zheltukhina
{"title":"On Construction of Darboux integrable discrete models","authors":"Kostyantyn Zheltukhin,&nbsp;Natalya Zheltukhina","doi":"10.1016/S0034-4877(23)00080-0","DOIUrl":"10.1016/S0034-4877(23)00080-0","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 3","pages":"Pages 279-289"},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","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}
引用次数: 0
Stäckel representations of stationary Kdv systems 静止 Kdv 系统的 Stäckel 表示法
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1016/S0034-4877(23)00083-6
Maciej Błaszak, Błażej M. Szablikowski, Krzysztof Marciniak
{"title":"Stäckel representations of stationary Kdv systems","authors":"Maciej Błaszak,&nbsp;Błażej M. Szablikowski,&nbsp;Krzysztof Marciniak","doi":"10.1016/S0034-4877(23)00083-6","DOIUrl":"10.1016/S0034-4877(23)00083-6","url":null,"abstract":"<div><div>In this article we study Stäckel representations of stationary KdV systems. 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.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 3","pages":"Pages 323-346"},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","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}
引用次数: 0
Magnetic Neumann Laplacian on a domain with a hole 带洞域上的磁性诺依曼拉普拉卡方
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1016/S0034-4877(23)00079-4
Diana Barseghyan , Baruch Schneider , Swanhild Bernstein
{"title":"Magnetic Neumann Laplacian on a domain with a hole","authors":"Diana Barseghyan ,&nbsp;Baruch Schneider ,&nbsp;Swanhild Bernstein","doi":"10.1016/S0034-4877(23)00079-4","DOIUrl":"10.1016/S0034-4877(23)00079-4","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 3","pages":"Pages 259-278"},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","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}
引用次数: 0
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