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On Exceptional Times for Pointwise Convergence of Integral Kernels in Feynman–Trotter Path Integrals Feynman-Trotter路径积分中积分核点收敛的例外时间
arXiv: Mathematical Physics Pub Date : 2020-04-13 DOI: 10.1007/978-3-030-61346-4_13
H. Feichtinger, F. Nicola, S. I. Trapasso
{"title":"On Exceptional Times for Pointwise Convergence of Integral Kernels in Feynman–Trotter Path Integrals","authors":"H. Feichtinger, F. Nicola, S. I. Trapasso","doi":"10.1007/978-3-030-61346-4_13","DOIUrl":"https://doi.org/10.1007/978-3-030-61346-4_13","url":null,"abstract":"","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84769703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Complete aggregation of the Lohe tensor model with the same free flow 完全聚合的Lohe张量模型具有相同的自由流
arXiv: Mathematical Physics Pub Date : 2020-04-11 DOI: 10.1063/5.0007292
Seung‐Yeal Ha, Hansol Park
{"title":"Complete aggregation of the Lohe tensor model with the same free flow","authors":"Seung‐Yeal Ha, Hansol Park","doi":"10.1063/5.0007292","DOIUrl":"https://doi.org/10.1063/5.0007292","url":null,"abstract":"The Lohe tensor model is a first-order tensor-valued continuous-time model for the aggregation of tensors with the same rank and size. It reduces to well-known aggregation models such as the Kuramoto model, the Lohe sphere model and the Lohe matrix model as special cases for low-rank tensors. We present a sufficient and necessary framework for the solution splitting property(SSP) and analyze two possible asymptotic states(completely aggregate state and bi-polar state) which can emerge from a set of initial data. Moreover, we provide a sufficient framework leading to the aforementioned two asymptotic states in terms of initial data and system parameters.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87650900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Linear Response and Analyticity 线性响应和分析
arXiv: Mathematical Physics Pub Date : 2020-04-08 DOI: 10.1007/978-3-030-39680-0_24
V. Balakrishnan
{"title":"Linear Response and Analyticity","authors":"V. Balakrishnan","doi":"10.1007/978-3-030-39680-0_24","DOIUrl":"https://doi.org/10.1007/978-3-030-39680-0_24","url":null,"abstract":"","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86600497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global hyperbolicity and factorization in cosmological models 宇宙学模型中的全局双曲和分解
arXiv: Mathematical Physics Pub Date : 2020-04-08 DOI: 10.1063/5.0038970
Zh. Avetisyan
{"title":"Global hyperbolicity and factorization in cosmological models","authors":"Zh. Avetisyan","doi":"10.1063/5.0038970","DOIUrl":"https://doi.org/10.1063/5.0038970","url":null,"abstract":"The geometry and topology of cosmological spacetimes and vector bundles thereon are discussed. Global hyperbolicty and factorization properties that are normally assumed in bulk in the literature are derived from a minimal set of assumptions using recent progress in pure mathematics.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77708686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Differential Invariants for Flows of Fluids and Gases 流体和气体流动的微分不变量
arXiv: Mathematical Physics Pub Date : 2020-04-03 DOI: 10.1007/978-3-030-63253-3_6
A. Duyunova, V. Lychagin, S. Tychkov
{"title":"Differential Invariants for Flows of Fluids and Gases","authors":"A. Duyunova, V. Lychagin, S. Tychkov","doi":"10.1007/978-3-030-63253-3_6","DOIUrl":"https://doi.org/10.1007/978-3-030-63253-3_6","url":null,"abstract":"","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77336687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Exact thresholds in the dynamics of cold plasma with electron-ion collisions 电子-离子碰撞冷等离子体动力学中的精确阈值
arXiv: Mathematical Physics Pub Date : 2020-04-02 DOI: 10.1063/5.0033619
O. Rozanova, E. Chizhonkov, Maria I. Delova
{"title":"Exact thresholds in the dynamics of cold plasma with electron-ion collisions","authors":"O. Rozanova, E. Chizhonkov, Maria I. Delova","doi":"10.1063/5.0033619","DOIUrl":"https://doi.org/10.1063/5.0033619","url":null,"abstract":"We consider a quasilinear system of hyperbolic equations that describes plane one-dimensional non-relativistic oscillations of electrons in a cold plasma with allowance for electron-ion collisions. Accounting for collisions leads to the appearance of a term analogous to dry friction in a mechanical system, leading to a decrease in the total energy. We obtain a criterion for the existence of a global in time smooth solution to the Cauchy problem. It allows to accurately separate the initial data into two classes: one corresponds to a globally in time smooth solutions, and the other leads to a finite-time blowup. The influence of electron collision frequency $ nu $ on the solution is investigated. It is shown that there is a threshold value, after exceeding which the regime of damped oscillations is replaced by the regime of monotonic damping. The set of initial data corresponding to a globally in time smooth solution of the Cauchy problem expands with increasing $ nu $, however, at an arbitrarily large value there are smooth initial data for which the solution forms a singularity in a finite time, and this time tends to zero as $ nu $ tends to infinity. The character of the emerging singularities is illustrated by numerical examples.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88589058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Hamiltonian multiform description of an integrable hierarchy 可积层次的哈密顿多形式描述
arXiv: Mathematical Physics Pub Date : 2020-04-02 DOI: 10.1063/5.0012153
V. Caudrelier, Matteo Stoppato
{"title":"Hamiltonian multiform description of an integrable hierarchy","authors":"V. Caudrelier, Matteo Stoppato","doi":"10.1063/5.0012153","DOIUrl":"https://doi.org/10.1063/5.0012153","url":null,"abstract":"Motivated by the notion of Lagrangian multiforms, which provide a Lagrangian formulation of integrability, and by results of the authors on the role of covariant Hamiltonian formalism for integrable field theories, we propose the notion of Hamiltonian multiforms for integrable $1+1$-dimensional field theories. They provide the Hamiltonian counterpart of Lagrangian multiforms and encapsulate in a single object an arbitrary number of flows within an integrable hierarchy. For a given hierarchy, taking a Lagrangian multiform as starting point, we provide a systematic construction of a Hamiltonian multiform based on a generalisation of techniques of covariant Hamiltonian field theory. This also produces two other important objects: a symplectic multiform and the related multi-time Poisson bracket. They reduce to a multisymplectic form and the related covariant Poisson bracket if we restrict our attention to a single flow in the hierarchy. Our framework offers an alternative approach to define and derive conservation laws for a hierarchy. We illustrate our results on three examples: the potential Korteweg-de Vries hierarchy, the sine-Gordon hierarchy (in light cone coordinates) and the Ablowitz-Kaup-Newell-Segur hierarchy.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87519973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Local algebras for causal fermion systems in Minkowski space Minkowski空间中因果费米子系统的局部代数
arXiv: Mathematical Physics Pub Date : 2020-04-01 DOI: 10.1063/5.0011371
F. Finster, Marco Oppio
{"title":"Local algebras for causal fermion systems in Minkowski space","authors":"F. Finster, Marco Oppio","doi":"10.1063/5.0011371","DOIUrl":"https://doi.org/10.1063/5.0011371","url":null,"abstract":"A notion of local algebras is introduced in the theory of causal fermion systems. Their properties are studied in the example of the regularized Dirac sea vacuum in Minkowski space. The commutation relations are worked out, and the differences to the canonical commutation relations are discussed. It is shown that the spacetime point operators associated to a Cauchy surface satisfy a time slice axiom. It is proven that the algebra generated by operators in an open set is irreducible as a consequence of Hegerfeldt's theorem. The light cone structure is recovered by analyzing expectation values of the operators in the algebra in the limit when the regularization is removed. It is shown that every spacetime point operator commutes with the algebras localized away from its null cone, up to small corrections involving the regularization length.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79440841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
SIMILARITY SOLUTIONS AND CONSERVATION LAWS FOR THE BEAM EQUATIONS: A COMPLETE STUDY 梁方程的相似解和守恒定律:一个完整的研究
arXiv: Mathematical Physics Pub Date : 2020-04-01 DOI: 10.14311/ap.2020.60.0098
Amlan K. Halder, A. Paliathanasis, P. Leach
{"title":"SIMILARITY SOLUTIONS AND CONSERVATION LAWS FOR THE BEAM EQUATIONS: A COMPLETE STUDY","authors":"Amlan K. Halder, A. Paliathanasis, P. Leach","doi":"10.14311/ap.2020.60.0098","DOIUrl":"https://doi.org/10.14311/ap.2020.60.0098","url":null,"abstract":"We study the similarity solutions and we determine the conservation laws of the various forms of beam equation, such as, Euler-Bernoulli, Rayleigh and Timoshenko-Prescott. The travelling-wave reduction leads to solvable fourth-order odes for all the forms. In addition, the reduction based on the scaling symmetry for the Euler-Bernoulli form leads to certain odes for which there exists zero symmetries. Therefore, we conduct the singularity analysis to ascertain the integrability. We study two reduced odes of order second and third. The reduced second-order ode is a perturbed form of Painleve-Ince equation, which is integrable and the third-order ode falls into the category of equations studied by Chazy, Bureau and Cosgrove. Moreover, we derived the symmetries and its corresponding reductions and conservation laws for the forced form of the above mentioned beam forms. The Lie Algebra is mentioned explicitly for all the cases.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89244862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Time-dependent propagator for an-harmonic oscillator with quartic term in potential 势为四次项的谐振子的时变传播子
arXiv: Mathematical Physics Pub Date : 2020-03-27 DOI: 10.1063/5.0018545
J. Boháčik, P. Prešnajder, P. August'in
{"title":"Time-dependent propagator for an-harmonic oscillator with quartic term in potential","authors":"J. Boháčik, P. Prešnajder, P. August'in","doi":"10.1063/5.0018545","DOIUrl":"https://doi.org/10.1063/5.0018545","url":null,"abstract":"In this work, we present the analytical approach to the evaluation of the conditional measure Wiener path integral. We consider the time-dependent model parameters. We find the differential equation for the variable, determining the behavior of the harmonic as well the an-harmonic parts of the oscillator. We present the an-harmonic part of the result in the form of the operator function.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79690121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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