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Graph limit of the consensus model with self-delay 具有自延迟的共识模型的图极限
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-13 DOI: 10.1088/1751-8121/ad6ab1
Jan Haskovec
{"title":"Graph limit of the consensus model with self-delay","authors":"Jan Haskovec","doi":"10.1088/1751-8121/ad6ab1","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6ab1","url":null,"abstract":"It is known that models of interacting agents with self-delay (reaction-type delay) do not admit, in general, the classical mean-field limit description in terms of a Fokker–Planck equation. In this paper we propose the graph limit of the nonlinear consensus model with self-delay as an alternative continuum description and study its mathematical properties. We establish the well-posedness of the resulting integro-differential equation in the Lebesgue <italic toggle=\"yes\">L<sup>p</sup></italic> space. We present a rigorous derivation of the graph limit from the discrete consensus system and derive a sufficient condition for reaching global asymptotic consensus. We also consider a linear variant of the model with a given interaction kernel, which can be interpreted as a dynamical system over a graphon. Here we derive an optimal (i.e. sufficient and necessary) condition for reaching global asymptotic consensus. Finally, we give a detailed explanation of how the presence of the self-delay term rules out a description of the mean-field limit in terms of a particle density governed by a Fokker–Planck-type equation. In particular, we show that the indistinguishability-of-particles property does not hold, which is one of the main ingredients for deriving the classical mean-field description.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"57 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Two protocols for telecloning of Bell-like states with and without ancilla qubit 有辅助比特和无辅助比特贝尔样态远程克隆的两种协议
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-13 DOI: 10.1088/1751-8121/ad6ab0
Binayak S Choudhury, Manoj Kumar Mandal, Soumen Samanta
{"title":"Two protocols for telecloning of Bell-like states with and without ancilla qubit","authors":"Binayak S Choudhury, Manoj Kumar Mandal, Soumen Samanta","doi":"10.1088/1751-8121/ad6ab0","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6ab0","url":null,"abstract":"The present work contains two telecloning protocols for obtaining approximately cloned copies of Bell-like states at two distant locations. The first one is a universal telecloning procedure utilizing ancilla qubits while in the second protocol, no ancilla qubit is required. The analysis of fidelity measuring the quality of the cloned copy is presented. Both the protocols are executed on the IBM platform using Aer Simulator as well as on quantum real computers. By comparing the outcomes of these two cases we conclude that both the protocols are robust.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"44 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Corrigendum: Gaussian fluctuations of the elephant random walk with gradually increasing memory (2024 J. Phys. A: Math. Theor. 57 065203) 更正：记忆逐渐增加的大象随机行走的高斯波动 (2024 J. Phys. A: Math. Theor. 57 065203)
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-12 DOI: 10.1088/1751-8121/ad6655
Rafik Aguech, Mohamed El Machkouri
{"title":"Corrigendum: Gaussian fluctuations of the elephant random walk with gradually increasing memory (2024 J. Phys. A: Math. Theor. 57 065203)","authors":"Rafik Aguech, Mohamed El Machkouri","doi":"10.1088/1751-8121/ad6655","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6655","url":null,"abstract":"The standard elephant random walk (ERW) is a discrete-time random walk introduced by Schütz and Trimper (2004 <italic toggle=\"yes\">Phys. Rev.</italic> E <bold>70</bold> 045101) with the particularity that the next step of the walker depends on its whole past through a parameter <inline-formula>\u0000<tex-math><?CDATA $pin[0,1]$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6655ieqn1.gif\"></inline-graphic></inline-formula>. In this note, we give a correction for the central limit theorem in the superdiffusive regime of the ERW with gradually increasing memory established by Aguech and El Machkouri (2024 <italic toggle=\"yes\">J. Phys. A: Math. Theor.</italic> <bold>57</bold> 065203, theorem 2). The mistake was pointed out by Roy <italic toggle=\"yes\">et al</italic> (2024 arXiv:2403.02881, remark 1.1).","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"22 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Mathematical analysis of bent optical waveguide eigenvalue problem 弯曲光波导特征值问题的数学分析
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-11 DOI: 10.1088/1751-8121/ad6aaf
Rakesh Kumar and Kirankumar R Hiremath
{"title":"Mathematical analysis of bent optical waveguide eigenvalue problem","authors":"Rakesh Kumar and Kirankumar R Hiremath","doi":"10.1088/1751-8121/ad6aaf","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6aaf","url":null,"abstract":"This work investigates a mathematical model of the propagation of lightwaves in bent optical waveguides. This modeling leads to a non-self-adjoint eigenvalue problem for differential operator defined on the unbounded domain. Through detailed analysis, a relationship between the real and imaginary parts of the complex-valued propagation constants was constructed. Using this relation, it is found that the real and imaginary parts of the propagation constants are bounded, meaning they are limited within certain region in the complex plane. The orthogonality of these bent modes is also proved. By the asymptotic analysis of these modes, it is proved that as the behavior of the eigenfunctions is proportional to","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"19 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Thermodynamics of a collisional quantum-dot machine: the role of stages 碰撞量子点机器的热力学：阶段的作用
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-08 DOI: 10.1088/1751-8121/ad695e
Fernando S Filho, C E Fernández Noa, Carlos E Fiore, B Wijns and B Cleuren
{"title":"Thermodynamics of a collisional quantum-dot machine: the role of stages","authors":"Fernando S Filho, C E Fernández Noa, Carlos E Fiore, B Wijns and B Cleuren","doi":"10.1088/1751-8121/ad695e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad695e","url":null,"abstract":"Sequential (or collisional) engines have been put forward as an alternative candidate for the realisation of reliable engine setups. Despite this, the role of the different stages and the influence of the intermediate reservoirs is not well understood. We introduce the idea of conveniently adjusting/choosing intermediate reservoirs at engine devices as a strategy for optimizing its performance. This is done by considering a minimal model composed of a quantum-dot machine sequentially exposed to various reservoirs at each stage, and for which thermodynamic quantities (including power and efficiency) can be obtained exactly from the framework of stochastic thermodynamics, irrespective the number of stages. Results show that a significant gain can be obtained by increasing the number of stages and conveniently choosing their parameters.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"8 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Membrane-in-the-middle optomechanical system and structural frequencies 膜中光学机械系统和结构频率
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-08 DOI: 10.1088/1751-8121/ad653e
Luis Pedro Lara, Ricardo Weder and Luis Octavio Castaños-Cervantes
{"title":"Membrane-in-the-middle optomechanical system and structural frequencies","authors":"Luis Pedro Lara, Ricardo Weder and Luis Octavio Castaños-Cervantes","doi":"10.1088/1751-8121/ad653e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad653e","url":null,"abstract":"We consider a one-dimensional membrane-in-the-middle model for a cavity that consists of two fixed, perfect mirrors and a mobile dielectric membrane between them that has a constant electric susceptibility. We present a sequence of exact cavity angular frequencies that we call structural angular frequencies and that have the remarkable property that they are independent of the position of the membrane inside the cavity. Furthermore, the case of a thin membrane is considered and simple, approximate formulae for the angular frequencies and for the modes of the cavity are obtained. Finally, the cavity electromagnetic potential is numerically calculated and it is found that the potential is accurately described by a multiple scales solution.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"2 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Computing distances on Riemann surfaces 计算黎曼曲面上的距离
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-07 DOI: 10.1088/1751-8121/ad653a
Huck Stepanyants, Alan Beardon, Jeremy Paton and Dmitri Krioukov
{"title":"Computing distances on Riemann surfaces","authors":"Huck Stepanyants, Alan Beardon, Jeremy Paton and Dmitri Krioukov","doi":"10.1088/1751-8121/ad653a","DOIUrl":"https://doi.org/10.1088/1751-8121/ad653a","url":null,"abstract":"Riemann surfaces are among the simplest and most basic geometric objects. They appear as key players in many branches of physics, mathematics, and other sciences. Despite their widespread significance, how to compute distances between pairs of points on compact Riemann surfaces is surprisingly unknown, unless the surface is a sphere or a torus. This is because on higher-genus surfaces, the distance formula involves an infimum over infinitely many terms, so it cannot be evaluated in practice. Here we derive a computable distance formula for a broad class of Riemann surfaces. The formula reduces the infimum to a minimum over an explicit set consisting of finitely many terms. We also develop a distance computation algorithm, which cannot be expressed as a formula, but which is more computationally efficient on surfaces with high genuses. We illustrate both the formula and the algorithm in application to generalized Bolza surfaces, which are a particular class of highly symmetric compact Riemann surfaces of any genus greater than 1.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"60 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
The duality between color and kinematics and its applications 色彩与运动学的二元性及其应用
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-07 DOI: 10.1088/1751-8121/ad5fd0
Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson and Radu Roiban
{"title":"The duality between color and kinematics and its applications","authors":"Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson and Radu Roiban","doi":"10.1088/1751-8121/ad5fd0","DOIUrl":"https://doi.org/10.1088/1751-8121/ad5fd0","url":null,"abstract":"This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to loop-level calculations, the broad web of theories linked by the duality and the associated double-copy structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"60 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Anomalous diffusion of self-propelled particles 自走粒子的反常扩散
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-04 DOI: 10.1088/1751-8121/ad6720
Francisco J Sevilla, Guillermo Chacón-Acosta and Trifce Sandev
{"title":"Anomalous diffusion of self-propelled particles","authors":"Francisco J Sevilla, Guillermo Chacón-Acosta and Trifce Sandev","doi":"10.1088/1751-8121/ad6720","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6720","url":null,"abstract":"The transport equation of active motion is generalised to consider time-fractional dynamics to describe the anomalous diffusion of self-propelled particles. In the present study, we consider an arbitrary active motion pattern modelled by a scattering function that defines the dynamics of the change of the self-propulsion direction. The exact probability density of the particle positions at a given time is obtained. From it, the time dependence of the firsts moments, i.e. the mean square displacement and the kurtosis for an arbitrary scattering function, are derived and analysed. Anomalous diffusion is found with a crossover of the scaling exponent from 2α in the short-time regime to α in the long-time one, being the order of the fractional derivative considered. It is shown that the exact solution found satisfies a fractional diffusion equation that accounts for the non-local and retarded effects of the Laplacian of the probability density function through a coupled temporal and spatial memory function. Such a memory function holds the complete information of the active-motion pattern. In the long-time regime, space and time are decoupled in the memory function, and the time fractional telegrapher’s equation is recovered. The theoretical framework presented here can be applied as model of active motion that exhibits anomalous diffusion.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"43 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
From the Fokker–Planck equation to a contact Hamiltonian system 从福克-普朗克方程到接触哈密顿系统
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-04 DOI: 10.1088/1751-8121/ad6225
Shin-itiro Goto
{"title":"From the Fokker–Planck equation to a contact Hamiltonian system","authors":"Shin-itiro Goto","doi":"10.1088/1751-8121/ad6225","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6225","url":null,"abstract":"The Fokker–Planck equation is one of the fundamental equations in nonequilibrium statistical mechanics, and this equation is known to be derived from the Wasserstein gradient flow equation with a free energy. This gradient flow equation describes relaxation processes and is formulated on a Riemannian manifold. Meanwhile contact Hamiltonian systems are also known to describe relaxation processes. Hence a relation between these two equations is expected to be clarified, which gives a solid foundation in geometric statistical mechanics. In this paper a class of contact Hamiltonian systems is derived from a class of the Fokker–Planck equations on Riemannian manifolds. In the course of the derivation, the Fokker–Planck equation is shown to be written as a diffusion equation with a weighted Laplacian without any approximation, which enables to employ a theory of eigenvalue problems.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"72 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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