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Fractional diffusion equations interpolate between damping and waves 分数扩散方程在阻尼和波浪之间进行插值
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-21 DOI: 10.1088/1751-8121/ad6c02
Andy Manapany, Sébastien Fumeron, Malte Henkel
{"title":"Fractional diffusion equations interpolate between damping and waves","authors":"Andy Manapany, Sébastien Fumeron, Malte Henkel","doi":"10.1088/1751-8121/ad6c02","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6c02","url":null,"abstract":"The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection–diffusion equation is also solved and an application to Pennes bioheat model is presented. Generically, a wave-like transport at short times passes over to a diffusion-like behaviour at later times.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186028","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
Estimating Bethe roots with VQE 用 VQE 估算贝特根
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-20 DOI: 10.1088/1751-8121/ad6db2
David Raveh, Rafael I Nepomechie
{"title":"Estimating Bethe roots with VQE","authors":"David Raveh, Rafael I Nepomechie","doi":"10.1088/1751-8121/ad6db2","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6db2","url":null,"abstract":"Bethe equations, whose solutions determine exact eigenvalues and eigenstates of corresponding integrable Hamiltonians, are generally hard to solve. We implement a Variational Quantum Eigensolver approach to estimating Bethe roots of the spin-1/2 XXZ quantum spin chain, by using Bethe states as trial states, and treating Bethe roots as variational parameters. In numerical simulations of systems of size up to 6, we obtain estimates for Bethe roots corresponding to both ground states and excited states with up to 5 down-spins, for both the closed and open XXZ chains. This approach is not limited to real Bethe roots.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186031","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
Nonlinear wave propagation in large extra spatial dimensions and the blackbody thermal laws 大额外空间维度中的非线性波传播与黑体热定律
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-14 DOI: 10.1088/1751-8121/ad6c03
I Soares, R Turcati, S B Duarte
{"title":"Nonlinear wave propagation in large extra spatial dimensions and the blackbody thermal laws","authors":"I Soares, R Turcati, S B Duarte","doi":"10.1088/1751-8121/ad6c03","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6c03","url":null,"abstract":"Nonlinear wave propagation in large extra spatial dimensions (on and above <italic toggle=\"yes\">d</italic> = 2) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant <inline-formula>\u0000<tex-math><?CDATA $mathscr{F}left( = -(1/4)F_{munu}F^{munu}right)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mi mathvariant=\"script\">F</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>4</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>F</mml:mi><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6c03ieqn1.gif\"></inline-graphic></inline-formula>. In this vein, we consider propagating waves under the influence of external uniform electric and magnetic fields. Features related to the blackbody radiation in the presence of a background constant electric field such as the generalization of the spectral energy density distribution and the Stefan–Boltzmann law are obtained. Interestingly enough, anisotropic contributions to the frequency spectrum appear in connection to the nonlinearity of the electromagnetic field. In addition, the long wavelength regime and Wien’s displacement law in this situation are studied. The corresponding thermodynamics quantities at thermal equilibrium, such as energy, pressure, entropy, and heat capacity densities are contemplated as well.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186030","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
Asymptotic behaviour of a phase field system derived from a generalization of Maxwell–Cattaneo’s law with a singular potential 由具有奇异势能的麦克斯韦-卡塔尼奥定律广义推导出的相场系统的渐近行为
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-14 DOI: 10.1088/1751-8121/ad6cb9
Brice Landry Doumbé Bangola, Mohamed Ali Ipopa, Armel Andami Ovono
{"title":"Asymptotic behaviour of a phase field system derived from a generalization of Maxwell–Cattaneo’s law with a singular potential","authors":"Brice Landry Doumbé Bangola, Mohamed Ali Ipopa, Armel Andami Ovono","doi":"10.1088/1751-8121/ad6cb9","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6cb9","url":null,"abstract":"In this paper, we study the asymptotic behaviour of a Caginalp-type phase field system derived from a heat conduction law which is a generalization of the Maxwell–Cattanéo law and whose potential is singular. This type of law has the advantage of correcting the paradox of heat conduction that appears when the Fourier law is considered. The potential considered is typically logarithmic. Using such a potential makes the model much more relevant from a physical point of view. However, from a theoretical point of view, it is essential to obtain the strict separation property of the phase field in order to give sense of the equations. We first prove the existence and uniqueness of the solution thanks to the separation property. We also address the question of the dissipativity of the system. Finally, we obtain the existence of the global attractor.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186032","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
Only-phase Popov action: thermodynamic derivation and superconducting electrodynamics 唯相波波夫作用：热力学推导和超导电动力学
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-14 DOI: 10.1088/1751-8121/ad6ab3
L Salasnich, M G Pelizzo, F Lorenzi
{"title":"Only-phase Popov action: thermodynamic derivation and superconducting electrodynamics","authors":"L Salasnich, M G Pelizzo, F Lorenzi","doi":"10.1088/1751-8121/ad6ab3","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6ab3","url":null,"abstract":"We provide a thermodynamic derivation of the only-phase Popov action functional, which is often adopted to study the low-energy effective hydrodynamics of a generic nonrelativistic superfluid. It is shown that the crucial assumption is the use of the saddle point approximation after neglecting the quantum-pressure term. As an application, we analyze charged superfluids (superconductors) coupled to the electromagnetic field at zero temperature. Our only-phase and minimally-coupled theory predicts the decay of the electrostatic field inside a superconductor with a characteristic length much smaller than the London penetration depth of the static magnetic field. This result is confirmed also by a relativistic only-phase Popov action we obtain from the Klein–Gordon Lagrangian.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186035","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
New characterization of Robertson–Walker geometries involving a single timelike curve 涉及单条时间曲线的罗伯逊-沃克几何图形的新特征
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-14 DOI: 10.1088/1751-8121/ad6ab6
Marc Mars, Raül Vera
{"title":"New characterization of Robertson–Walker geometries involving a single timelike curve","authors":"Marc Mars, Raül Vera","doi":"10.1088/1751-8121/ad6ab6","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6ab6","url":null,"abstract":"Our aim in this paper is two-fold. We establish a novel geometric characterization of the Robertson–Walker (RW) spacetime and, along the process, we find a canonical form of the RW metric associated to an arbitrary timelike curve and an arbitrary space frame. A known characterization establishes that a spacetime foliated by constant curvature leaves whose orthogonal flow (the cosmological flow) is geodesic, shear-free, and with constant expansion on each leaf, is RW. We generalize this characterization by relaxing the condition on the expansion. We show it suffices to demand that the spatial gradient and Laplacian of the cosmological expansion on a single arbitrary timelike curve vanish. In General Relativity these local conditions are equivalent to demanding that the energy flux measured by the cosmological flow, as well as its divergence, are zero on a single arbitrary timelike curve. The proof allows us to construct canonically adapted coordinates to the arbitrary curve, thus well-fitted to an observer with an arbitrary motion with respect to the cosmological flow.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186039","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
How much symmetry do symmetric measurements need for efficient operational applications? 对称测量需要多大的对称性才能实现高效的操作应用？
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-14 DOI: 10.1088/1751-8121/ad6cb8
Katarzyna Siudzińska
{"title":"How much symmetry do symmetric measurements need for efficient operational applications?","authors":"Katarzyna Siudzińska","doi":"10.1088/1751-8121/ad6cb8","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6cb8","url":null,"abstract":"We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). This provides a uniform description of objects that are more general than symmetric, informationally complete POVMs and mutually unbiased bases, but at the same time less destructive and more noise tolerant. For informationally complete sets, we propose construction methods from orthonormal Hermitian operator bases. The correspondence between operator bases and measurements can be as high as one-to-four, with a one-to-one correspondence following only under additional assumptions. Importantly, it turns out that some of the symmetry properties, lost in the process of generalization, can be recovered without fixing the same number of elements for all POVMs. In particular, for a wide class of unequinumerous symmetric measurements that are conical 2-designs, we derive the index of coincidence, entropic uncertainty relations, and separability criteria for bipartite quantum states.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186034","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
Heterogeneous mean-field analysis of the generalized Lotka–Volterra model on a network 网络上广义洛特卡-伏特拉模型的异质均场分析
IF 2.1 3区 物理与天体物理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-13 DOI: 10.1088/1751-8121/ad6ab2
Fabián Aguirre-López
{"title":"Heterogeneous mean-field analysis of the generalized Lotka–Volterra model on a network","authors":"Fabián Aguirre-López","doi":"10.1088/1751-8121/ad6ab2","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6ab2","url":null,"abstract":"We study the dynamics of the generalized Lotka–Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us to describe the fixed points of the model in terms of a few simple order parameters. We extend the analysis even for diverging abundances, using a mapping to the replicator model. With this we present a unified approach for both cooperative and competitive systems that display complementary behaviors. In particular we show the central role of an order parameter called the critical degree, <inline-formula>\u0000<tex-math><?CDATA $g_mathrm{c}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6ab2ieqn1.gif\"></inline-graphic></inline-formula>. In the competitive regime <inline-formula>\u0000<tex-math><?CDATA $g_mathrm{c}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"aad6ab2ieqn2.gif\"></inline-graphic></inline-formula> serves to distinguish high degree nodes that are more likely to go extinct, while in the cooperative regime it has the reverse role, it will determine the low degree nodes that tend to go relatively extinct.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186038","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
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":null,"pages":null},"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":null,"pages":null},"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
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