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Critical behavior of dirty free parafermionic chains 脏自由副费米子链的临界行为
IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-07-24 DOI: 10.1088/1751-8121/ad6723
Akshat Pandey, Aditya Cowsik
A family of $mathbb Z_n$-symmetric non-Hermitian models of Baxter was shown by Fendley to be exactly solvable via a parafermionic generalization of the Clifford algebra. We study these models with spatially random couplings, and obtain several exact results on thermodynamic singularities as the distributions of couplings are varied. We find that these singularities, independent of $n$, are identical to those in the random transverse-field Ising chain; correspondingly the models host infinite-randomness critical points. Similarities in structure to exact methods for random Ising models, a strong-disorder renormalization group, and generalizations to other models with free spectra, are discussed.
芬德利(Fendley)通过克利福德代数的对位费米子广义化证明了巴克斯特的 $mathbb Z_n$ 对称非赫米特模型族是可以精确求解的。我们研究了这些具有空间随机耦合的模型,并获得了随着耦合分布的变化而出现的热力学奇点的若干精确结果。我们发现,这些奇点与 $n$ 无关,与随机横向场伊辛链中的奇点相同;相应地,模型中存在无限随机临界点。我们讨论了与随机伊辛模型精确方法、强无序重正化群结构的相似性,以及对其他具有自由光谱模型的推广。
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引用次数: 0
Response theory identifies reaction coordinates and explains critical phenomena in noisy interacting systems 反应理论确定反应坐标,解释嘈杂互动系统中的临界现象
IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-07-24 DOI: 10.1088/1751-8121/ad6068
N Zagli, V Lucarini and G A Pavliotis
We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We identify mathematical conditions on the microscopic interaction structure, namely the separability of the interaction kernel, that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates (RCs). Such RCs prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the RCs. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems.
我们考虑了一类具有成对相互作用和淬火无序动力学特征的非平衡系统,该系统在热力学极限下具有相变特征。我们确定了微观相互作用结构的数学条件,即相互作用内核的可分离性,从而以有限数量的反应坐标(RC)来降低系统的维度。这些反应坐标被证明是适当的非平衡热力学变量,因为它们承载着系统的相关性、记忆性和复原性信息。相变可以通过与 RC 相关的复值易感性函数的奇异性来识别和定量表征。我们提供了奇点如何影响有限尺寸系统物理特性的分析和数值证据。
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引用次数: 0
Quantum fluctuation dynamics of open quantum systems with collective operator-valued rates, and applications to Hopfield-like networks 具有集体算子值速率的开放量子系统的量子波动动力学及其在类霍普菲尔德网络中的应用
IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-07-24 DOI: 10.1088/1751-8121/ad6363
Eliana Fiorelli
We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the dissipation features local transitions that depend on collective, operator-valued rates, encoding average properties of the system. These types of generators can be formally obtained by generalizing, to the quantum realm, classical (mean-field) stochastic Markov dynamics, with state-dependent transitions. Focusing on the dynamics emerging in the limit of infinitely large systems, we build on the exactness of the mean-field equations for the dynamics of average operators. In this framework, we derive the dynamics of quantum fluctuation operators, that can be used in turn to understand the fate of quantum correlations in the system. We then apply our results to quantum generalized Hopfield associative memories. Here we show that, asymptotically and at the description level of quantum fluctuations, only a very weak amount of quantum correlations, in the form of quantum discord, emerges beyond classical correlations.
我们考虑了一类以马尔可夫方式演化的开放量子多体系统,其动力学发生器为 GKS-Lindblad 形式。在这里,哈密顿贡献的特点是全对全耦合,耗散的特点是局部转变,取决于集体的、算子值的速率,编码系统的平均特性。这些类型的发生器可以通过将经典(均场)随机马尔可夫动力学推广到量子领域而正式获得,并具有与状态相关的转换。我们将重点放在无限大系统极限中出现的动力学上,以平均算子动力学的均值场方程的精确性为基础。在此框架下,我们推导出了量子波动算子的动力学,并可反过来用于理解系统中量子相关性的命运。然后,我们将结果应用于量子广义 Hopfield 关联记忆。我们在这里证明,在量子波动的描述层面上,只有非常微弱的量子相关性(以量子不和的形式)会出现在经典相关性之外。
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引用次数: 0
Can N-th Order Born Approximation Be Exact? N-阶天生近似能否精确?
IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-07-24 DOI: 10.1088/1751-8121/ad66c1
F. Loran, A. Mostafazadeh
For the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions, we identify a condition on the scattering interaction under which the N-th order Born approximation gives the exact solution of the scattering problem for some N ≥ 1.
对于二维和三维标量波以及三维电磁波的散射,我们确定了散射相互作用的一个条件,在此条件下,N-阶博恩近似给出了某个 N ≥ 1 的散射问题的精确解。
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引用次数: 0
Ratchet-mediated resetting: current, efficiency, and exact solution 以棘轮为媒介的复位:电流、效率和精确解
IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-07-23 DOI: 10.1088/1751-8121/ad62c9
Connor Roberts, Emir Sezik and Eloise Lardet
We model an overdamped Brownian particle that is subject to resetting facilitated by a ratchet potential on a spatially periodic domain. This asymmetric potential switches on with a constant rate, but switches off again only upon the particle’s first passage to a resetting point at the minimum of the potential. Repeating this cycle sustains a non-equilibrium steady-state, as well as a directed steady-state current which can be harnessed to perform useful work. We derive exact analytic expressions for the probability densities of the free-diffusion and resetting phases, the associated currents for each phase, and an efficiency parameter that quantifies the return in current for given power input. These expressions allow us to fully characterise the system and obtain experimentally relevant results such as the optimal current and efficiency. Our results are corroborated by simulations, and have implications for experimentally viable finite-time resetting protocols.
我们模拟了一个过阻尼布朗粒子的模型,该粒子在空间周期域上受到棘轮势的重置。这种非对称电势以恒定的速率开启,但只有当粒子第一次到达电势最小值处的重置点时才会再次关闭。重复这一循环可维持非平衡稳态以及定向稳态电流,利用定向稳态电流可进行有用功。我们推导出了自由扩散和复位阶段的概率密度、每个阶段的相关电流以及量化给定功率输入下电流回报的效率参数的精确解析表达式。通过这些表达式,我们可以全面描述系统特性,并获得与实验相关的结果,如最佳电流和效率。我们的结果得到了模拟的证实,并对实验可行的有限时间复位协议产生了影响。
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引用次数: 0
Interference aided finite resonant response in an undamped forced oscillator 无阻尼强迫振荡器中的干涉辅助有限共振响应
IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-07-23 DOI: 10.1088/1751-8121/ad6412
Shihabul Haque and Jayanta K Bhattacharjee
We apply perturbative techniques to a driven undamped sinusoidal oscillator at resonance. The angular displacement, θ, obeys the dynamics . The linearized approximation gives a divergent response (at long times) but the nonlinear terms make the response finite. We address the nonlinearity-induced finiteness in two ways by separately treating the short and long time scales. At long times, we use the traditional perturbative techniques to extract two drive dependent behaviours—one, the amplitude of oscillation scales as and, two, the time period of the slow mode varies as . For the early time behaviour, on the other hand, we devise an alternate perturbative expansion where the successive terms get larger with the order of evaluation but have alternating signs. The alternating signs (phase differences) between these terms leads to adestructive interference like effect. A careful consideration of this destructive interference like effect between successive terms leads to a finite response which describes the initial behaviour of the amplitude of the response reasonably correctly. We further note that for larger drive values, the system seems to undergo a first order transitional behaviour with a sudden jump in the largest Lyapunov exponent
我们将微扰技术应用于共振时的驱动无阻尼正弦振荡器。角位移 θ 遵循动力学原理。线性化近似给出了发散响应(长时间),但非线性项使响应有限。我们通过分别处理短时标和长时标两种方法来解决非线性引起的有限性问题。在长时间尺度上,我们使用传统的扰动技术来提取两种与驱动力相关的行为--一是振荡幅度随时间变化;二是慢模的时间周期随时间变化。另一方面,对于早期时间行为,我们设计了另一种扰动扩展,在这种扩展中,连续项随着求值阶数的增加而增大,但具有交替的符号。这些项之间的交替符号(相位差)会导致破坏性干扰效应。仔细考虑连续项之间的这种破坏性干扰效应,就会得出一个有限响应,它能合理正确地描述响应振幅的初始特性。我们还注意到,当驱动力值较大时,系统似乎会出现一阶过渡行为,最大的李雅普诺夫指数会突然跃升
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引用次数: 0
The effect of Skyrme–Chern–Simons dynamics on gauged Skyrmions in 2+1 dimensions Skyrme-Chern-Simons 动力学对 2+1 维测量 Skyrmions 的影响
IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-07-23 DOI: 10.1088/1751-8121/ad61d4
Francisco Navarro-Lérida, Eugen Radu and D H Tchrakian
We study the Skyrmion of the SO(2) gauged O(3) sigma model in dimensions in the presence of a Skyrme–Chern–Simons (SCS) term, and compare its properties with the corresponding properties of the Skyrmion in the presence of the usual Chern–Simons (CS) term. We find that these properties are qualitatively largely similar in both cases, meaning that the SCS density can be employed as an alternative to the CS term also in higher dimensions, most importantly in even dimensions where no CS term is defined, in dimensions. The SCS density employed here is defined in terms of the pair of gauge fields and an auxiliary O(5) Skyrme scalar, which is contracted to an effective O(3) Skyrme scalar. Technically, this study maps the methods to be applied in higher dimensional examples.
我们研究了SO(2)测量O(3)西格玛模型在维度上存在Skyrme-Chern-Simons(SCS)项时的Skyrmion,并将其性质与存在通常的Chern-Simons(CS)项时的Skyrmion的相应性质进行了比较。我们发现,这两种情况下的性质大体相似,这意味着在更高的维度上,最重要的是在没有定义 CS 项的维度上,也可以用 SCS 密度来替代 CS 项。这里采用的SCS密度是根据一对规量场和一个辅助的O(5) Skyrme标量定义的,它被收缩为一个有效的O(3) Skyrme标量。从技术上讲,这项研究将这些方法映射到了更高维度的例子中。
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引用次数: 0
Algebraic formulas and geometric derivation of source identities 源等式的代数公式和几何推导
IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-07-23 DOI: 10.1088/1751-8121/ad62c8
Kohei Motegi and Ryo Ohkawa
Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant representations for source functions which appeared in previous literature as well as introducing the elliptic version of the determinants, and obtain identities between determinants. We also show several symmetrization formulas for the rational version.
源等式是多元特殊函数之间的基本等式。我们给出了有理函数和三角函数源等式的几何推导。我们还对以前文献中出现的源函数的各种行列式表示进行了系统的推导和扩展,并引入了行列式的椭圆版本,获得了行列式之间的同构关系。我们还展示了有理版的几个对称公式。
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引用次数: 0
The Unruh–DeWitt model and its joint interacting Hilbert space 恩鲁-德威特模型及其联合作用希尔伯特空间
IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-07-23 DOI: 10.1088/1751-8121/ad6365
Erickson Tjoa and Finnian Gray
In this work we make the connection between the Unruh–DeWitt (UDW) particle detector model applied to quantum field theory in curved spacetimes and the rigorous construction of the spin-boson (SB) model. With some modifications, we show that existing results about the existence of a SB ground state can be adapted to the UDW model. In the most relevant scenario involving massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes, where the UDW model describes a simplified model of light–matter interaction, we argue that common choices of the spacetime smearing functions regulate the ultraviolet behaviour of the model but can still exhibit infrared (IR) divergences. In particular, this implies the well-known expectation that the joint interacting Hilbert space of the model cannot be described by the tensor product of a two-dimensional complex Hilbert space and the Fock space of the vacuum representation. We discuss the conditions under which this problem does not arise and the relevance of the operator-algebraic approach for better understanding of particle detector models and their applications.Our work clarifies the connection between obstructions due to Haag’s theorem and IR bosons in the SB models, and paves the way for more rigorous study of entanglement and communication in the UDW framework involving multiple detectors.
在这项研究中,我们将应用于弯曲时空量子场论的 Unruh-DeWitt (UDW)粒子探测器模型与自旋玻色子(SB)模型的严格构建联系起来。经过一些修改,我们证明现有的关于 SB 基态存在的结果可以适用于 UDW 模型。在涉及(3+1)维全局双曲时空中无质量标量场的最相关情景中,UDW 模型描述了光-物质相互作用的简化模型,我们认为时空涂抹函数的常见选择可以调节模型的紫外行为,但仍然会表现出红外发散。特别是,这意味着模型的联合相互作用希尔伯特空间不能用二维复希尔伯特空间和真空表示的福克空间的张量乘积来描述这一众所周知的预期。我们的研究澄清了哈格定理和 SB 模型中的红外玻色子所导致的障碍之间的联系,并为在涉及多个探测器的 UDW 框架中更严格地研究纠缠和通信铺平了道路。
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引用次数: 0
Multi-parameter quantum estimation of single- and two-mode pure Gaussian states 单模和双模纯高斯状态的多参数量子估算
IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Pub Date : 2024-07-22 DOI: 10.1088/1751-8121/ad6364
Gabriele Bressanini, Marco G Genoni, M S Kim and Matteo G A Paris
We discuss the ultimate precision bounds on the multiparameter estimation of single- and two-mode pure Gaussian states. By leveraging on previous approaches that focused on the estimation of a complex displacement only, we derive the Holevo Cramér–Rao bound (HCRB) for both displacement and squeezing parameter characterizing single and two-mode squeezed states. In the single-mode scenario, we obtain an analytical bound and find that it degrades monotonically as the squeezing increases. Furthermore, we prove that heterodyne detection is nearly optimal in the large squeezing limit, but in general the optimal measurement must include non-Gaussian resources. On the other hand, in the two-mode setting, the HCRB improves as the squeezing parameter grows and we show that it can be attained using double-homodyne detection.
我们讨论了单模和双模纯高斯状态多参数估计的最终精度界限。通过利用以前只关注复位移估计的方法,我们推导出了描述单模和双模挤压态的位移和挤压参数的 Holevo Cramér-Rao 约束 (HCRB)。在单模情况下,我们得到了一个分析约束,并发现它随着挤压的增加而单调退化。此外,我们还证明,在大挤压极限下,外差探测几乎是最优的,但一般来说,最优测量必须包括非高斯资源。另一方面,在双模式设置中,HCRB 会随着挤压参数的增加而改善,我们还证明了可以通过双同调检测来达到这一目标。
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引用次数: 0
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Journal of Physics A: Mathematical and Theoretical
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