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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 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-08-21 DOI: 10.1088/1751-8121/ad6c02
Andy Manapany, Sébastien Fumeron, Malte Henkel
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.
研究了基于卡普托导数的时间分数扩散方程的解的行为,并分析了其对分数指数的依赖性。此外,还求解了时间分数对流扩散方程,并介绍了该方程在 Pennes 生物热模型中的应用。一般来说,短时间内的波状传输会在后期转变为扩散行为。
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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 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-08-20 DOI: 10.1088/1751-8121/ad6db2
David Raveh, Rafael I Nepomechie
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.
贝特方程的解决定了相应可积分哈密顿的精确特征值和特征状态,但通常很难求解。我们采用变分量子伊根求解器(Variational Quantum Eigensolver)方法,将贝特态作为试验态,并将贝特根作为变分参数来估计自旋-1/2 XXZ 量子自旋链的贝特根。在对最多 6 个系统的数值模拟中,我们获得了闭合和开放 XXZ 链的贝特根的估计值,这些贝特根对应于基态和具有最多 5 个下旋的激发态。这种方法并不局限于实贝特根。
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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 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-08-14 DOI: 10.1088/1751-8121/ad6c03
I Soares, R Turcati, S B Duarte
Nonlinear wave propagation in large extra spatial dimensions (on and above d = 2) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant F(=(1/4)FμνFμν). 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.
我们在非线性电动力学理论的背景下研究了大额外空间维度(d = 2 及以上)的非线性波传播,这些理论完全依赖于不变量 F(=-(1/4)FμνFμν)。因此,我们考虑的是在外部均匀电场和磁场影响下传播的波。我们得到了存在背景恒定电场时黑体辐射的相关特征,如光谱能量密度分布的广义化和斯蒂芬-玻尔兹曼定律。有趣的是,频谱的各向异性贡献与电磁场的非线性有关。此外,还研究了这种情况下的长波长制度和维恩位移定律。还考虑了热平衡时的相应热力学量,如能量、压力、熵和热容量密度。
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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 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-08-14 DOI: 10.1088/1751-8121/ad6cb9
Brice Landry Doumbé Bangola, Mohamed Ali Ipopa, Armel Andami Ovono
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.
在本文中,我们研究了一个卡吉纳普型相场系统的渐近行为,该系统由热传导定律衍生而来,而热传导定律是麦克斯韦-卡塔内奥定律的一般化,其势能是奇异的。这种定律的优点是纠正了在考虑傅立叶定律时出现的热传导悖论。所考虑的电势通常是对数。从物理角度来看,使用这种势能使模型更加贴切。然而,从理论角度来看,必须获得相场的严格分离特性,才能使方程具有意义。我们首先利用分离特性证明了解的存在性和唯一性。我们还讨论了系统的耗散性问题。最后,我们得到了全局吸引子的存在性。
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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 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-08-14 DOI: 10.1088/1751-8121/ad6ab3
L Salasnich, M G Pelizzo, F Lorenzi
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.
我们提供了唯一相波波夫作用函数的热力学推导,它通常被用来研究一般非相对论超流体的低能有效流体力学。研究表明,关键的假设是在忽略量子压力项之后使用鞍点近似。作为应用,我们分析了零温度下与电磁场耦合的带电超流体(超导体)。我们的唯相和最小耦合理论预测了超导体内部静电场的衰减,其特征长度远小于静磁场的伦敦穿透深度。我们从克莱因-戈登拉格朗日得到的相对论性唯相波波夫作用也证实了这一结果。
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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 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-08-14 DOI: 10.1088/1751-8121/ad6ab6
Marc Mars, Raül Vera
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.
本文的目的有两个方面。我们建立了罗伯逊-沃克(RW)时空的新几何特征,并在此过程中找到了与任意时间曲线和任意空间框架相关的 RW 度量的典型形式。一个已知的特征是,一个由恒定曲率叶片构成的时空,其正交流(宇宙学流)是测地的、无剪切的,并且在每个叶片上都有恒定的扩展,那么这个时空就是 RW 时空。我们通过放宽膨胀条件来概括这一特征。我们证明,只需要求宇宙膨胀在一条任意时间曲线上的空间梯度和拉普拉斯消失即可。在广义相对论中,这些局部条件等同于要求宇宙学流测量的能量通量及其发散在一条任意时间曲线上为零。通过证明,我们可以构建与任意曲线相适应的坐标,从而很好地适应相对于宇宙学流的任意运动的观测者。
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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 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-08-14 DOI: 10.1088/1751-8121/ad6cb8
Katarzyna Siudzińska
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.
我们将对称测量推广到不等量的正算子值测量(POVMs)集合。这提供了对对象的统一描述,它比对称、信息完整的 POVMs 和互不偏倚基更为通用,但同时破坏性更小,对噪声的容忍度更高。对于信息完全集,我们提出了正交赫米特算子基的构造方法。算子基与测量之间的对应关系可高达一比四,只有在额外的假设条件下才能实现一一对应。重要的是,事实证明,在泛化过程中丢失的一些对称特性可以在不固定所有 POVM 的相同元素数的情况下恢复。特别是,对于一大类锥形 2 设计的不等量对称测量,我们推导出了重合指数、熵不确定性关系以及双方量子态的可分性准则。
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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 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-08-13 DOI: 10.1088/1751-8121/ad6ab2
Fabián Aguirre-López
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, gc. In the competitive regime gc 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.
我们研究了具有网络结构的广义 Lotka-Volterra 模型的动力学。通过对图形进行高连接性扩展,我们写出了包含度异质性的均场动力学理论。这样,我们就能用几个简单的阶次参数来描述模型的定点。我们利用复制器模型的映射,扩展了对发散丰度的分析。这样,我们就为显示互补行为的合作和竞争系统提供了一种统一的方法。我们特别展示了一个称为临界度 gc 的阶次参数的核心作用。在竞争系统中,临界值 gc 的作用是区分更有可能消亡的高程度节点,而在合作系统中,它的作用正好相反,它将决定倾向于相对消亡的低程度节点。
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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 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-08-13 DOI: 10.1088/1751-8121/ad6ab1
Jan Haskovec
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 Lp 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.
众所周知,具有自延时(反应型延时)的相互作用者模型一般不采用福克-普朗克方程的经典均场极限描述。在本文中,我们提出了具有自延迟的非线性共识模型的图极限,作为另一种连续描述,并研究了它的数学特性。我们在 Lebesgue Lp 空间中建立了所得到的积分微分方程的好求解性。我们对离散共识系统的图极限进行了严格推导,并得出了达成全局渐近共识的充分条件。我们还考虑了具有给定交互核的线性模型变体,它可以被解释为图元上的动力系统。在这里,我们得出了达成全局渐近共识的最优(即充分和必要)条件。最后,我们详细解释了自延迟项的存在如何排除了用福克-普朗克方程式的粒子密度来描述均场极限。特别是,我们证明了粒子的不可分性特性不成立,而这正是推导经典均场描述的主要因素之一。
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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 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-08-13 DOI: 10.1088/1751-8121/ad6ab0
Binayak S Choudhury, Manoj Kumar Mandal, Soumen Samanta
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.
本研究包含两个远距离克隆协议,用于在两个遥远的地点获得类似贝尔状态的近似克隆拷贝。第一个是利用 ancilla 量子位的通用远程克隆程序,而在第二个协议中,不需要 ancilla 量子位。对克隆副本质量的保真度进行了分析。这两个协议都是在 IBM 平台上使用 Aer 模拟器和量子真实计算机执行的。通过比较这两种情况的结果,我们得出结论:这两个协议都很稳健。
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引用次数: 0
期刊
Journal of Physics A: Mathematical and Theoretical
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