数学物理
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- [1] arXiv:2510.14334 [中文pdf, pdf, html, 其他]
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标题： 静电计算在统计力学和随机矩阵应用中的研究标题： Electrostatic computations for statistical mechanics and random matrix applications评论： 35页主题： 数学物理 (math-ph)
尽管大部分内容是经典的，静电学的主题至今仍有许多新的应用。 在本文中，我们突出介绍了几项关于静电学的理论结果，这些结果既用于说明一般原理，也用于统计力学和随机矩阵设置中的应用。 理论结果包括一般维度中球体和超椭球体相关的静电势和能量，二维情况下的共形映射的应用，以及扫除测度。 给出了它们在预测某些配置积分和特定统计力学系统中粒子密度的主导渐近形式中的显式例子，以及与波动公式和（条件）间隙概率相关问题的讨论。
Although for the most part classical, the topic of electrostatics finds to this day new applications. In this review we highlight several theoretical results on electrostatics, chosen to both illustrate general principles, and for their application in statistical mechanics and random matrix settings. The theoretical results include electrostatic potentials and energies associated with balls and hyperellipsoids in general dimension, the use of conformal mappings in two-dimensions, and the balayage measure. A number of explicit examples of their use in predicting the leading asymptotic form of certain configuration integrals and particle density in particular statistical mechanical systems are given, as well as with regards to questions relating to fluctuation formulas and (conditioned) gap probabilities.
- [2] arXiv:2510.14764 [中文pdf, pdf, html, 其他]
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标题： 量子基尼兹尼克-扎莫洛德奇科夫方程与时间依赖相互作用强度的量子场论的可积性标题： Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-dependent Interaction Strength主题： 数学物理 (math-ph) ; 强关联电子 (cond-mat.str-el) ; 高能物理 - 理论 (hep-th)
在本文中，我们考虑解决具有时间依赖相互作用强度的量子场论问题。 我们表明，最近提出的框架[P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)]，这是常规Bethe假设技术的推广，提供了精确的多体波函数。 在此框架中，时间依赖的薛定谔方程被简化为一组解析差分方程和矩阵差分方程，称为量子Knizhnik-Zamolodchikov（qKZ）方程。 解的一致性导致对时间依赖相互作用强度的约束。 对于满足这些约束的相互作用强度，系统是可积的，qKZ方程和解析差分方程的解提供了满足时间依赖薛定谔方程的多体波函数的显式形式。 我们通过考虑具有时间依赖相互作用强度的$SU(2)$Gross-Neveu模型提供了一个具体例子。 使用此框架，我们解决了具有最一般时间依赖相互作用强度的模型，并得到了波函数的显式形式。
In this paper we consider the problem of solving quantum field theories with time dependent interaction strengths. We show that the recently formulated framework [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)], which is a generalization of the regular Bethe ansatz technique, provides the exact many-body wavefunction. In this framework, the time-dependent Schrodinger equation is reduced to a set of analytic difference equations and matrix difference equations, called the quantum Knizhnik-Zamolodchikov (qKZ) equations. The consistency of the solution gives rise to constraints on the time-dependent interaction strengths. For interaction strengths satisfying these constraints, the system is integrable, and the solution to the qKZ and the analytic difference equations provides the explicit form of the many-body wavefunction that satisfies the time-dependent Schrodinger equation. We provide a concrete example by considering the $SU(2)$ Gross-Neveu model with time dependent interaction strength. Using this framework we solve the model with the most general time-dependent interaction strength and obtain the explicit form of the wave function.
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- [3] arXiv:2510.13881 (交叉列表自 physics.bio-ph) [中文pdf, pdf, html, 其他]
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标题： 通过量子库仑势的低能DNA气泡动力学标题： Low-Energy DNA Bubble Dynamics via the Quantum Coulomb Potential主题： 生物物理 (physics.bio-ph) ; 软凝聚态物理 (cond-mat.soft) ; 数学物理 (math-ph)
我们开发了一个低能模型，可以在任何时间用于描述熔点以下温度下DNA气泡的动力学。 与这个问题相关的薛定谔方程在虚时间中用量子库仑势求解，并且我们得到了其更一般的物理解的近似表达式，作为能量接近下限能量的状态的线性组合。 然后我们可以根据贝塞尔函数确定概率密度、首次通过时间密度和关联函数。 我们的发现与直接从福克-普朗克方程得到的结果一致。 与伽马和扩散模型的比较进行了讨论。
We developed a low-energy model that can be used at any time to describe the dynamics of DNA bubbles at temperatures below the melting point. The Schr\"odinger equation associated with this problem is solved in imaginary time with a quantum Coulomb potential, and we obtain an approximate expression for its more general physical solution as a linear combination of the states whose energies are close to the lower bound energy. We can then determine the probability density, the first-passage time density, and the correlation functions in terms of Bessel functions. Our findings are consistent with results obtained directly from the Fokker-Planck equation. Comparisons with the Gamma and Diffusion models are discussed.
- [4] arXiv:2510.13980 (交叉列表自 quant-ph) [中文pdf, pdf, html, 其他]
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标题： 顺序量子测量与仪器群代数标题： Sequential Quantum Measurements and the Instrumental Group Algebra评论： 43页，5张表格主题： 量子物理 (quant-ph) ; 数学物理 (math-ph)
许多最基本的可观测量 | 位置、动量、相点和自旋方向 | 无法通过遵循正交投影假设的仪器进行测量。 连续时间测量提供了缺失的理论框架，以理解这些可观测量。 时变仪器的元素定义了一个称为\emph{工具组}（IG）的群。 相对于 IG，所有的时变性都包含在一个称为\emph{Kraus算子密度}（KOD）的函数中，该函数根据经典的柯尔莫哥洛夫方程演化。 与林德布洛德主方程不同，KOD 柯尔莫哥洛夫方程直接表达了仪器元素（而不仅仅是总信道）如何演化。 从连续测量转向更一般的顺序测量，显示按顺序组合仪器的结构对应于它们的 KOD 的卷积。 这种卷积将 IG 提升为\emph{乘法巴拿赫代数}（一种可以追溯到 POVM 和 C*-代数理论起源的结构），这将被称为\emph{工具群代数}（IGA）。 IGA 是 KOD 的真正家园，类似于冯·诺依曼代数的对偶是密度算子的家园。 作用在 IGA 上的算子，对于 KOD 的作用类似于超算符对于密度算子的作用，被称为\emph{超算子}，并讨论了各种例子。 考虑了一些超算符-超算符交织关系，包括 KOD 柯尔莫哥洛夫方程与林德布洛德主方程之间的关系。 还表明 IGA 实际上有两个对合：一个被卷积超算符尊重，另一个被量子信道超算符尊重。 最后，推导了跳跃过程和更一般的扩散过程的 KOD 柯尔莫哥洛夫生成元。
Many of the most fundamental observables | position, momentum, phase-point, and spin-direction | cannot be measured by an instrument that obeys the orthogonal projection postulate. Continuous-in-time measurements provide the missing theoretical framework to make sense of such observables. The elements of the time-dependent instrument define a group called the \emph{instrumental group} (IG). Relative to the IG, all of the time-dependence is contained in a certain function called the \emph{Kraus-operator density} (KOD), which evolves according to a classical Kolmogorov equation. Unlike the Lindblad master equation, the KOD Kolmogorov equation is a direct expression of how the elements of the instrument (not just the total channel) evolve. Shifting from continuous measurement to sequential measurements more generally, the structure of combining instruments in sequence is shown to correspond to the convolution of their KODs. This convolution promotes the IG to an \emph{involutive Banach algebra} (a structure that goes all the way back to the origins of POVM and C*-algebra theory) which will be called the \emph{instrumental group algebra} (IGA). The IGA is the true home of the KOD, similar to how the dual of a von Neumann algebra is the home of the density operator. Operators on the IGA, which play the same role for KODs as superoperators play for density operators, are called \emph{ultraoperators} and various examples are discussed. Certain ultraoperator-superoperator intertwining relations are considered, including the relation between the KOD Kolmogorov equation and the Lindblad master equation. The IGA is also shown to have actually two involutions: one respected by the convolution ultraoperators and the other by the quantum channel superoperators. Finally, the KOD Kolmogorov generators are derived for jump processes and more general diffusive processes.
- [5] arXiv:2510.14132 (交叉列表自 physics.chem-ph) [中文pdf, pdf, html, 其他]
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标题： 阴影分子动力学用于柔性多极模型标题： Shadow Molecular Dynamics for Flexible Multipole Models主题： 化学物理 (physics.chem-ph) ; 数学物理 (math-ph)
阴影分子动力学为具有长程静电相互作用的柔性电荷模型提供了一个高效且稳定的原子模拟框架。 尽管之前的实现仅限于原子单极电荷分布，但我们将其扩展到柔性多极模型。 我们推导了阴影能量函数、势能和力项的详细表达式，明确包含了单极-单极、偶极-单极和偶极-偶极相互作用。 在我们的公式中，原子单极和原子偶极都被视为与核自由度传播一起的扩展动力学变量。 我们证明，引入额外的偶极自由度可以保持在仅含单极的阴影分子动力学模拟中之前观察到的稳定性和准确性。 此外，我们提出了一种阴影分子动力学方案，在该方案中，单极电荷被固定，而偶极则保持灵活。 我们扩展的阴影动力学提供了一个框架，用于涉及柔性多极之间长程相互作用的稳定、计算高效且通用的分子动力学模拟。 这在与现代人工智能和机器学习技术结合时尤为重要，这些技术正越来越多地用于开发物理信息和数据驱动的基础模型，用于原子模拟。 这些模型旨在提供可转移的、高精度的原子相互作用表示，适用于各种分子系统，这需要对长程电荷相互作用进行准确处理。
Shadow molecular dynamics provide an efficient and stable atomistic simulation framework for flexible charge models with long-range electrostatic interactions. While previous implementations have been limited to atomic monopole charge distributions, we extend this approach to flexible multipole models. We derive detailed expressions for the shadow energy functions, potentials, and force terms, explicitly incorporating monopole-monopole, dipole-monopole, and dipole-dipole interactions. In our formulation, both atomic monopoles and atomic dipoles are treated as extended dynamical variables alongside the propagation of the nuclear degrees of freedom. We demonstrate that introducing the additional dipole degrees of freedom preserves the stability and accuracy previously seen in monopole-only shadow molecular dynamics simulations. Additionally, we present a shadow molecular dynamics scheme where the monopole charges are held fixed while the dipoles remain flexible. Our extended shadow dynamics provide a framework for stable, computationally efficient, and versatile molecular dynamics simulations involving long-range interactions between flexible multipoles. This is of particular interest in combination with modern artificial intelligence and machine learning techniques, which are increasingly used to develop physics-informed and data-driven foundation models for atomistic simulations. These models aim to provide transferable, high-accuracy representations of atomic interactions that are applicable across diverse sets of molecular systems, which requires accurate treatment of long-range charge interactions.
- [6] arXiv:2510.14170 (交叉列表自 hep-th) [中文pdf, pdf, html, 其他]
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标题： 大-$N$ Yang-Mills理论中的扭量威尔逊环标题： Twistor Wilson loops in large-$N$ Yang-Mills theory评论： 26页，无图主题： 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph)
多年来已知，在具有$\mathcal{N}=4,2,2^*$超对称的杨-米尔斯理论中，存在某些非平凡的超对称威尔逊环，其真空期望值要么是平凡的，要么可以通过来自上同调场论的局部化方法计算，该上同调场论也计算$\mathcal{N}=2,2^*$理论中的非微扰预势。 此外，几年前有人指出，类似于超对称情况，某些非平凡的扭量威尔逊环在纯 SU($N$) 杨-米尔斯理论中存在，其真空期望值在大$N$阶次下是平凡的，并且在大$N$阶次下由一个拓扑场论/弦理论计算，该理论在次领头$\frac{1}{N}$阶次下，推测能够捕捉胶球谱和胶球一环有效作用量的非微扰信息。 事实上，独立于上述内容，也有人声称“每个具有质量间隙的规范理论在红外区应包含可能平凡的拓扑场论”，因此上述扭量威尔逊环实现了这一观点的更强版本，因为它们的真空期望值在所有能量尺度下都是平凡的，而不仅仅是在红外区。 在本文中，我们提供了对杨-米尔斯理论中扭量威尔逊环真空期望值在大$N$阶次下的平凡性的详细证明，此前仅进行了简要说明，为进一步的发展开辟了道路。
It has been known for many years that, in Yang-Mills theories with $\mathcal{N}=4,2,2^*$ supersymmetry, certain nontrivial supersymmetric Wilson loops exist with v.e.v. either trivial or computable by localization that arises from a cohomological field theory, which also computes the nonperturbative prepotential in $\mathcal{N}=2,2^*$ theories. Moreover, some years ago it has been argued that, in analogy with the supersymmetric case, certain nontrivial twistor Wilson loops with trivial v.e.v. to the leading large-$N$ order exist in pure SU($N$) Yang-Mills theory and are computed, to the leading large-$N$ order, by a topological field/string theory that, to the next-to-leading $\frac{1}{N}$ order, conjecturally captures nonperturbative information on the glueball spectrum and glueball one-loop effective action as well. In fact, independently of the above, it has also been claimed that "every gauge theory with a mass gap should contain a possibly trivial topological field theory in the infrared", so that the aforementioned twistor Wilson loops realize a stronger version of this idea, as they have trivial v.e.v. at all energy scales and not only in the infrared. In the present paper, we provide a detailed proof of the triviality of the v.e.v. of twistor Wilson loops at the leading large-$N$ order in Yang-Mills theory that has previously been only sketched, opening the way to further developments.
- [7] arXiv:2510.14228 (交叉列表自 gr-qc) [中文pdf, pdf, html, 其他]
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标题： 大爆炸时临界弗里德曼时空的不稳定性作为暗能量的替代方案标题： The Instability of the Critical Friedmann Spacetime at the Big Bang as an Alternative to Dark Energy主题： 广义相对论与量子宇宙学 (gr-qc) ; 数学物理 (math-ph)
我们表征了无压弗里德曼时空在大爆炸时对径向扰动的局部不稳定性。 分析基于在自相似变量$(t,\xi)$中的爱因斯坦-欧拉方程表述，其中$\xi=r/t$被设计用来将临界（$k=0$）弗里德曼时空作为驻定解，其作为不稳定鞍点的性质$SM$通过光滑解在$\xi$的偶次幂展开来确定。 $SM$的特征值表明，$k\neq0$弗里德曼时空是$SM$不稳定流形内的不稳定解。 我们证明了所有在对称中心平滑的解在$\xi$的领先阶上与弗里德曼时空一致，并且为了关注宇宙学，我们关注$\mathcal{F}$，即在领先阶上与$k<0$弗里德曼时空一致的解集，提供了通用的低密度径向扰动在不稳定的临界弗里德曼时空下演化的最大族。 我们证明在中间时间，$\mathcal{F}$中的解通常会加速远离弗里德曼时空，但会衰减回到相同的主阶弗里德曼时空，作为$t\to\infty$的渐近行为。因此，爱因斯坦-欧拉方程中的不稳定性提供了一种自然机制，用于加速膨胀，而无需借助宇宙常数或暗能量。
We characterize the local instability of pressureless Friedmann spacetimes to radial perturbation at the Big Bang. The analysis is based on a formulation of the Einstein-Euler equations in self-similar variables $(t,\xi)$, with $\xi=r/t$, conceived to realize the critical ($k=0$) Friedmann spacetime as a stationary solution whose character as an unstable saddle rest point $SM$ is determined via an expansion of smooth solutions in even powers of $\xi$. The eigenvalues of $SM$ imply the $k\neq0$ Friedmann spacetimes are unstable solutions within the unstable manifold of $SM$. We prove that all solutions smooth at the center of symmetry agree with a Friedmann spacetime at leading order in $\xi$, and with an eye toward Cosmology, we focus on $\mathcal{F}$, the set of solutions which agree with a $k<0$ Friedmann spacetime at leading order, providing the maximal family into which generic underdense radial perturbations of the unstable critical Friedmann spacetime will evolve. We prove solutions in $\mathcal{F}$ generically accelerate away from Friedmann spacetimes at intermediate times but decay back to the same leading order Friedmann spacetime asymptotically as $t\to\infty$. Thus instabilities inherent in the Einstein-Euler equations provide a natural mechanism for an accelerated expansion without recourse to a cosmological constant or dark energy.
- [8] arXiv:2510.14433 (交叉列表自 cond-mat.stat-mech) [中文pdf, pdf, html, 其他]
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标题： 大型Dyson指数下的Tracy-Widom分布标题： The Tracy-Widom distribution at large Dyson index评论： 37页，6图主题： 统计力学 (cond-mat.stat-mech) ; 无序系统与神经网络 (cond-mat.dis-nn) ; 数学物理 (math-ph)
We study the Tracy-Widom (TW) distribution $f_\beta(a)$ in the limit of large Dyson index $\beta \to +\infty$. This distribution describes the fluctuations of the rescaled largest eigenvalue $a_1$ of the Gaussian (alias Hermite) ensemble (G$\beta$E) of (infinitely) large random matrices. We show that, at large $\beta$, its probability density function takes the large deviation form $f_\beta(a) \sim e^{-\beta \Phi(a)}$. 虽然$a_1$在其均值周围的典型偏差是方差为$O(1/\beta)$的高斯分布，但这种大偏差形式描述了偏差为$O(1)$的罕见事件的概率，并支配了高阶累积量的行为。 我们得到速率函数$\Phi(a)$作为 Painlevé II 方程的解。 我们推导出其大参数行为的显式公式，以及直到四阶的最低累积量。 我们对所有$a$数值计算$\Phi(a)$，并将其与有限$\beta$时的 TW 分布的精确数值计算进行比较。 这些结果是通过对与能量级$E=-a$相关的问题应用鞍点近似得到的，该问题由随机量子哈密顿量定义，该哈密顿量由随机Airy算子（SAO）给出。 我们采用了两种互补的方法：(i) 我们使用最优波动方法来找到在基态能量为$E$的条件下SAO中的噪声最可能实现；(ii) 我们将弱噪声理论应用于与SAO相关的Ricatti扩散过程表示的TW分布。 我们将结果扩展到整个Airy点过程$a_1>a_2>\dots$，它描述了G$\beta$E的所有边缘本征值，并对应于SAO的（负的）更高能量级，得到了$a_i$边缘分布的大偏差形式，联合分布和间隔分布。
We study the Tracy-Widom (TW) distribution $f_\beta(a)$ in the limit of large Dyson index $\beta \to +\infty$. This distribution describes the fluctuations of the rescaled largest eigenvalue $a_1$ of the Gaussian (alias Hermite) ensemble (G$\beta$E) of (infinitely) large random matrices. We show that, at large $\beta$, its probability density function takes the large deviation form $f_\beta(a) \sim e^{-\beta \Phi(a)}$. While the typical deviation of $a_1$ around its mean is Gaussian of variance $O(1/\beta)$, this large deviation form describes the probability of rare events with deviation $O(1)$, and governs the behavior of the higher cumulants. We obtain the rate function $\Phi(a)$ as a solution of a Painlev\'{e} II equation. We derive explicit formula for its large argument behavior, and for the lowest cumulants, up to order 4. We compute $\Phi(a)$ numerically for all $a$ and compare with exact numerical computations of the TW distribution at finite $\beta$. These results are obtained by applying saddle-point approximations to an associated problem of energy levels $E=-a$, for a random quantum Hamiltonian defined by the stochastic Airy operator (SAO). We employ two complementary approaches: (i) we use the optimal fluctuation method to find the most likely realization of the noise in the SAO, conditioned on its ground-state energy being $E$ (ii) we apply the weak-noise theory to the representation of the TW distribution in terms of a Ricatti diffusion process associated to the SAO. We extend our results to the full Airy point process $a_1>a_2>\dots$ which describes all edge eigenvalues of the G$\beta$E, and correspond to (minus) the higher energy levels of the SAO, obtaining large deviation forms for the marginal distribution of $a_i$, the joint distributions, and the gap distributions.
- [9] arXiv:2510.14461 (交叉列表自 math.AP) [中文pdf, pdf, 其他]
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标题： 小时间对数薛定谔方程的近似能控性标题： Small-time approximate controllability of the logarithmic Schr\''dinger equation主题： 偏微分方程分析 (math.AP) ; 数学物理 (math-ph) ; 优化与控制 (math.OC) ; 量子物理 (quant-ph)
我们考虑在$\mathbb{T}^d$或$\mathbb{R}^d$上的具有对数非线性和双线性控制的薛定谔方程。 我们证明了它们的小时间全局$L^2$-近似可控性。 证明是将由第一作者和第三作者在\cite{beauchard-pozzoli2}中为控制线性方程所引入的方法扩展到这种非线性框架：它结合了相位和梯度流的小时间可控性。 由于非线性，所需的估计比在线性情况下更难建立。 这里的证明受到WKB分析的启发。 这是首次针对具有双线性控制的非线性薛定谔方程的（小时间）全局近似可控性的结果。
We consider Schr{\"o}dinger equations with logarithmic nonlinearity and bilinear controls, posed on $\mathbb{T}^d$ or $\mathbb{R}^d$. We prove their small-time global $L^2$-approximate controllability. The proof consists in extending to this nonlinear framework the approach introduced by the first and third authors in \cite{beauchard-pozzoli2} to control the linear equation: it combines the small-time controllability of phases and gradient flows. Due to the nonlinearity, the required estimates are more difficult to establish than in the linear case. The proof here is inspired by WKB analysis. This is the first result of (small-time) global approximate controllability, for nonlinear Schr{\"o}dinger equations, with bilinear controls.
- [10] arXiv:2510.14472 (交叉列表自 nlin.SI) [中文pdf, pdf, html, 其他]
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标题： 非对称可积湍流和导数非线性薛定谔方程的 rogue 波统计特性标题： Asymmetric integrable turbulence and rogue wave statistics for the derivative nonlinear Schrödinger equation评论： 22页，12图主题： 精确可解与可积系统 (nlin.SI) ; 数学物理 (math-ph) ; 模式形成与孤子 (nlin.PS) ; 计算物理 (physics.comp-ph) ; 流体动力学 (physics.flu-dyn)
我们研究了DNLS方程中平面波的调制不稳定性（MI）所产生的非对称可积湍流和异常波（RWs）。 \(n\)阶矩和系综平均的动能和势能表现出向稳态值振荡收敛。 具体而言，这些指标的振幅随时间以\(t^{-1.36}\)的方式渐近衰减，而相位偏移则以\(t^{-0.78}\)的速率呈现非线性衰减。 这些振荡的频率被观察到是MI最大增长率的两倍。 这些振荡可以分为两种不同的类型：一种与系综平均势能模$|\langle H_4\rangle|$同相，另一种则为反相。 同时，这种统一性也体现在给定\( k \)的波作用谱\( S_k(t) \)、给定\( x \)的自相关函数\( g(x,t) \)以及概率密度函数\( P(I,t) \)上。 湍流的关键特征是波作用谱，它遵循幂律分布\( |k+3|^{-\alpha} \)，除了$k=-3$。 与NLS方程不同，DNLS设置中的湍流是不对称的，主要是由于来自MI的平面波的波数与扰动波数之间的不对称性。当\( S_k \)的渐近峰值出现在\( k = -3 \)时，自相关函数在\( x \to \pm L/2 \)处表现出非零水平。波强度的PDF以振荡方式渐近接近指数分布。然而，在非线性相位的初始阶段，MI略微增加了RWs的发生率。这发生在势模处于最小值的时刻，此时在\( I\in [12, 15] \)范围内的RWs发生概率明显高于渐近稳态情况。
We investigate the asymmetric integrable turbulence and rogue waves (RWs) emerging from the modulation instability (MI) of plane waves for the DNLS equation. The \(n\)-th moments and ensemble-averaged kinetic and potential energy exhibit oscillatory convergence towards their steady-state values. Specifically, the amplitudes of oscillations for these indexes decay asymptotically with time as \(t^{-1.36}\), while the phase shifts demonstrate a nonlinear decay with a rate of \(t^{-0.78}\). The frequency of these oscillations is observed to be twice the maximum growth rate of MI. These oscillations can be classified into two distinct types: one is in phase with ensemble-averaged potential energy modulus $|\langle H_4\rangle|$, and the other is anti-phase. At the same time, this unity is also reflected in the wave-action spectrum \( S_k(t) \) for a given \( k \), the auto-correlation function \( g(x,t) \) for a given \( x \), as well as the PDF \( P(I,t) \). The critical feature of the turbulence is the wave-action spectrum, which follows a power-law distribution of \( |k+3|^{-\alpha} \) expect for $k=-3$. Unlike the NLS equation, the turbulence in the DNLS setting is asymmetric, primarily due to the asymmetry between the wave number of the plane wave from the MI and the perturbation wave number.. As the asymptotic peak value of \( S_k \) is observed at \( k = -3 \), the auto-correlation function exhibits a nonzero level as \( x \to \pm L/2 \). The PDF of the wave intensity asymptotically approaches the exponential distribution in an oscillatory manner. However, during the initial stage of the nonlinear phase, MI slightly increases the occurrence of RWs. This happens at the moments when the potential modulus is at its minimum, where the probability of RWs occurring in the range of \( I\in [12, 15] \) is significantly higher than in the asymptotic steady state.
- [11] arXiv:2510.14483 (交叉列表自 hep-th) [中文pdf, pdf, html, 其他]
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标题： 量子上同调的tt*结构对于复数格拉斯曼流形标题： The tt*-structure for the quantum cohomology of complex Grassmannian评论： 29页主题： 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph)
tt*-方程（拓扑-反拓扑融合方程）由S. Cecotti和C. Vafa引入，用于描述超对称共形场理论的非零质量扰动。 B. Dubrovin将tt*-方程表述为一个平坦丛，称为tt*-结构。 在本文中，我们构造了复数\(k\)-平面的Grassmannian的量子上同调的tt*-结构，并按照Bourdeau的想法得到了tt*-方程的全局解。 我们通过使用偏微分方程理论以及J. Dorfmeister、F. Pedit和H. Wu（DPW方法）发展的调和映射理论，给出了精确的数学表述和解的描述。 此外，我们给出了复数射影空间的量子上同调的tt*-结构的第\(k\)次外积的tt*-结构与Grassmannian的量子上同调的tt*-结构之间的同构。
The tt*-equation (topological-anti-topological fusion equation) was introduced by S. Cecotti and C. Vafa for describing massive deformation of supersymmetric conformal field theories. B. Dubrovin formulated the tt*-equation as a flat bundle, called tt*-structure. In this paper, we construct a tt*-structure for the quantum cohomology of the Grassmannian of complex \(k\)-plane and obtain global solutions to the tt*-equation, following the idea of Bourdeau. We give a precise mathematical formulation and a description of the solutions by using p.d.e. theory and the harmonic map theory developed by J. Dorfmeister, F. Pedit and H. Wu (the DPW method). Furthermore, we give an isomorphism between tt*-structure for the \(k\)-th exterior product of tt*-structure for the quantum cohomology of the complex projective space and the tt*-structure for the quantum cohomology of the Grassmannian.
- [12] arXiv:2510.14679 (交叉列表自 cond-mat.quant-gas) [中文pdf, pdf, html, 其他]
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标题： 非线性朗道能级在近似玻色子任意子气体中标题： Nonlinear Landau levels in the almost-bosonic anyon gas评论： 17页，包括参考文献、补充材料、4张图表和14张数值数据表主题： 量子气体 (cond-mat.quant-gas) ; 数学物理 (math-ph) ; 量子物理 (quant-ph)
我们考虑平面中相互作用的阿贝尔任意子多粒子气体的定量描述，该气体被限制在势阱中。 如果任意子被建模为带有磁通量附加的玻色子，并且总磁通量相对于粒子数较小，则平均场描述适用于气体的低能集体态。 具体而言，通过哈特里-贾斯特罗假设，我们推导出一个两参数的陈-西蒙斯-薛定谔能量泛函，该泛函将众所周知的格罗斯-皮塔耶夫斯基/非线性薛定谔密度泛函理论扩展到磁（任意子）自相互作用。 一个参数决定了系统中自生成磁通量单位的总数，另一个参数决定了自旋轨道自相互作用的有效强度。 这种后一种相互作用可以是吸引/聚焦或排斥/散焦，并且既取决于内在的自旋轨道相互作用，也取决于任意子磁通分布的相对长度尺度。 对于参数的广泛范围，研究了基态和激发态的密度和能量，并与描述杰基夫-皮自对偶孤子的一系列精确非线性兰道能级一致。 随着磁通量的增加，形成反向旋转的涡旋，增强了气体对抗塌缩的稳定性。 除了澄清文献中出现的各种不同任意子模型之间的关系外，我们的分析为多任意子谱问题提供了大量新的见解，并且也举例说明了一种新颖的超对称性破缺现象。
We consider the quantitative description of a many-particle gas of interacting abelian anyons in the plane, confined in a trapping potential. If the anyons are modeled as bosons with a magnetic flux attachment, and if the total magnetic flux is small compared to the number of particles, then an average-field description becomes appropriate for the low-energy collective state of the gas. Namely, by means of a Hartree-Jastrow ansatz, we derive a two-parameter Chern-Simons-Schr\"odinger energy functional which extends the well-known Gross-Pitaevskii / nonlinear Schr\"odinger density functional theory to the magnetic (anyonic) self-interaction. One parameter determines the total number of self-generated magnetic flux units in the system, and the other the effective strength of spin-orbit self-interaction. This latter interaction can be either attractive/focusing or repulsive/defocusing, and depends both on the intrinsic spin-orbit interaction and the relative length scale of the flux profile of the anyons. Densities and energies of ground and excited states are studied analytically and numerically for a wide range of the parameters and align well with a sequence of exact nonlinear Landau levels describing Jackiw-Pi self-dual solitons. With increasing flux, counter-rotating vortices are formed, enhancing the stability of the gas against collapse. Apart from clarifying the relations between various different anyon models that have appeared in the literature, our analysis sheds considerable new light on the many-anyon spectral problem, and also exemplifies a novel supersymmetry-breaking phenomenon.
- [13] arXiv:2510.14817 (交叉列表自 quant-ph) [中文pdf, pdf, html, 其他]
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标题： 噪声量子模拟器上的拓扑对称性签名标题： Signatures of Topological Symmetries on a Noisy Quantum Simulator评论： 6页，4图主题： 量子物理 (quant-ph) ; 统计力学 (cond-mat.stat-mech) ; 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph)
拓扑对称性，无论是否可逆，在量子场论的研究中起着基础性作用。 尽管它们在从弦理论到凝聚态物理等多个学科中具有普遍的重要性，但在物理系统中可控地实现表现出这些对称性的模型却很少。 基于工程化固态器件的量子模拟器为实现这些模型提供了一种新颖的替代方案，与传统的凝聚态系统不同。 在本工作中，二维时空中的伊辛共形场理论相关的杂质哈密顿量和环算符的本征态，以及与拓扑对称性相关的本征态，在IBM的Kingston模拟器上得到了实现。 相关状态是通过一种混合量子-经典算法在量子设备上创建的。 该算法基于量子近似优化算法的变体，并结合了量子自然梯度优化方法。 通过测量不同量子比特算符的相关函数，并将结果与量子设备的结果进行比较，捕捉到了拓扑对称性的特征，结果与经典计算的结果基本一致。 当前的工作展示了噪声量子模拟器作为研究低维量子场论的平台的可行性，并能够直接访问在传统凝聚态实验中通常难以探测的可观测量。
Topological symmetries, invertible and otherwise, play a fundamental role in the investigation of quantum field theories. Despite their ubiquitous importance across a multitude of disciplines ranging from string theory to condensed matter physics, controlled realizations of models exhibiting these symmetries in physical systems are rare. Quantum simulators based on engineered solid-state devices provide a novel alternative to conventional condensed matter systems for realizing these models. In this work, eigenstates of impurity Hamiltonians and loop operators associated with the topological symmetries for the Ising conformal field theory in two space-time dimensions are realized on IBM's Kingston simulator. The relevant states are created on the quantum device using a hybrid quantum-classical algorithm. The latter is based on a variation of the quantum approximate optimization algorithm ansatz combined with the quantum natural gradient optimization method. Signatures of the topological symmetry are captured by measuring correlation functions of different qubit operators with results obtained from the quantum device in reasonable agreement with those obtained from classical computations. The current work demonstrates the viability of noisy quantum simulators as platforms for investigating low-dimensional quantum field theories with direct access to observables that are often difficult to probe in conventional condensed matter experiments.
交叉提交 (展示 11 之 11 条目 )
- [14] arXiv:2411.17036 (替换) [中文pdf, pdf, html, 其他]
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标题： 聚焦非线性薛定谔方程孤立子的随机集的大数定律和中心极限定理标题： Law of Large Numbers and Central Limit Theorem for random sets of solitons of the focusing nonlinear Schrödinger equation评论： 26页，1图主题： 数学物理 (math-ph) ; 偏微分方程分析 (math.AP) ; 概率 (math.PR) ; 模式形成与孤子 (nlin.PS) ; 精确可解与可积系统 (nlin.SI)
We study a random configuration of $N$ soliton solutions $\psi_N(x,t;\boldsymbol{\lambda})$ of the cubic focusing Nonlinear Schrödinger (fNLS) equation in one space dimension. The $N$ soliton solutions are parametrized by $2N$ complex numbers $(\boldsymbol{\lambda}, \boldsymbol{c})$ where $\boldsymbol{\lambda}\in\mathbb{C}_+^N$ are the eigenvalues of the Zakharov-Shabat linear operator, and $ \boldsymbol{c}\in\mathbb{C}^N\backslash \{0\}$ are the norming constants of the corresponding eigenfunctions. The randomness is obtained by choosing the complex eigenvalues to be i.i.d. random variables sampled from a probability distribution with compact support in the complex plane. The corresponding norming constants are interpolated by a smooth function of the eigenvalues. Then we consider the expectation of the random measure associated to this random spectral data. 这种期望通过Zakharov-Shabat逆谱问题唯一地确定了fNLS方程的解$\psi_\infty(x,t)$。 这个解可以被解释为孤子气体解。 我们证明了当$(x,t)$位于$\mathbb R\times\mathbb R^+$的一个紧集内时，差值$\psi_N(x,t;\boldsymbol{\lambda})-\psi_\infty(x,t)$和$|\psi_N(x,t;\boldsymbol{\lambda})|^2-|\psi_\infty(x,t)|^2$满足大数定律和中心极限定理；我们还计算了关联函数。
We study a random configuration of $N$ soliton solutions $\psi_N(x,t;\boldsymbol{\lambda})$ of the cubic focusing Nonlinear Schr\"odinger (fNLS) equation in one space dimension. The $N$ soliton solutions are parametrized by $2N$ complex numbers $(\boldsymbol{\lambda}, \boldsymbol{c})$ where $\boldsymbol{\lambda}\in\mathbb{C}_+^N$ are the eigenvalues of the Zakharov-Shabat linear operator, and $ \boldsymbol{c}\in\mathbb{C}^N\backslash \{0\}$ are the norming constants of the corresponding eigenfunctions. The randomness is obtained by choosing the complex eigenvalues to be i.i.d. random variables sampled from a probability distribution with compact support in the complex plane. The corresponding norming constants are interpolated by a smooth function of the eigenvalues. Then we consider the expectation of the random measure associated to this random spectral data. Such expectation uniquely identifies, via the Zakharov-Shabat inverse spectral problem, a solution $\psi_\infty(x,t)$ of the fNLS equation. This solution can be interpreted as a soliton gas solution. We prove a Law of Large Numbers and a Central Limit Theorem for the differences $\psi_N(x,t;\boldsymbol{\lambda})-\psi_\infty(x,t)$ and $|\psi_N(x,t;\boldsymbol{\lambda})|^2-|\psi_\infty(x,t)|^2$ when $(x,t)$ are in a compact set of $\mathbb R\times\mathbb R^+$; we additionally compute the correlation functions.
- [15] arXiv:2510.13092 (替换) [中文pdf, pdf, html, 其他]
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标题： 关于高斯$β$系列最优软边扩张的注记标题： A Note on Optimal Soft Edge Expansions for the Gaussian $β$ Ensembles评论： 6页，研究成果源自MATRIX项目合作 “天际的气体”主题： 数学物理 (math-ph)
我们提供一些与随机矩阵理论中$\beta$系统相关联的关联函数和相关可观测量最优渐近展开的专题综述材料。 我们还对目前正在开展的一个相关研究领域进行了介绍。
We present some review material relating to the topic of optimal asymptotic expansions of correlation functions and associated observables for $\beta$ ensembles in random matrix theory. We also give an introduction to a related line of study that we are presently undertaking.
- [16] arXiv:2403.12947 (替换) [中文pdf, pdf, html, 其他]
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标题： 量子过程的可恢复性的基本限制标题： Fundamental limitations on the recoverability of quantum processes评论： 改进的展示（接近发表版本）；有关在量子热力学中的应用，请参见 https://arxiv.org/abs/2510.12790 (arXiv:2510.12790)期刊参考： 安娜les Henri Poincaré，2025主题： 量子物理 (quant-ph) ; 数学物理 (math-ph)
量子信息处理和计算任务可以被理解为量子网络，包括量子态和信道以及它们可能经历的物理变换。 因此，估计量子过程在经历物理变换时信息内容的变化是相关的。 量子态的物理变换由量子信道描述，而量子信道的变换由量子超信道描述。 在本工作中，我们确定了如何良好地撤销或逆转量子信道上的物理变换的基本限制，这些限制对于设计和评估量子信息和计算设备至关重要。 特别是，我们在量子超信道的作用下，对量子信道的量子数据处理不等式进行了改进（加强）。 我们识别了一类量子超信道，它似乎是在量子超信道作用下的子单位量子信道的超信道类比，在这种作用下，任意量子信道的熵是非递减的。 我们还提供了在任意量子超信道作用下量子信道熵变化的改进不等式。
Quantum information processing and computing tasks can be understood as quantum networks, comprising quantum states and channels and possible physical transformations on them. It is hence pertinent to estimate the change in informational content of quantum processes due to physical transformations they undergo. The physical transformations of quantum states are described by quantum channels, while the transformations of quantum channels are described by quantum superchannels. In this work, we determine fundamental limitations on how well the physical transformation on quantum channels can be undone or reversed, which are of crucial interest to design and benchmark quantum information and computation devices. In particular, we refine (strengthen) the quantum data processing inequality for quantum channels under the action of quantum superchannels. We identify a class of quantum superchannels, which appears to be the superchannel analogue of subunital quantum channels, under the action of which the entropy of an arbitrary quantum channel is nondecreasing. We also provide a refined inequality for the entropy change of quantum channels under the action of an arbitrary quantum superchannel.
- [17] arXiv:2412.12328 (替换) [中文pdf, pdf, html, 其他]
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标题： AdS$N$体问题在大自旋情况下标题： AdS $N$-body problem at large spin评论： 74页+附录，19图；v2：发表版本主题： 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph)
受一般CFT中多旋量算符问题的启发，我们研究了大自旋下AdS中$N$体问题的主导旋量态$J$。 我们发现对于大多数态，有效的量子力学问题变为半经典问题，其中$\hbar=1/J$。 在$J=\infty$处的经典系统具有$N-2$自由度，经典相空间被识别为正格拉斯曼ian$\mathrm{Gr}_{+}(2,N)$。 通过经典哈密顿量的贝雷津-托普利茨量子化，可以恢复量子问题，我们对此进行了详细描述。 对于$N=3$，经典系统有一个自由度，可以通过玻尔-索末菲条件获得谱的详细结构。 对于所有$N$，我们证明最低的激发态可由简谐振子近似，并找到了它们能量的显式表达式。
Motivated by the problem of multi-twist operators in general CFTs, we study the leading-twist states of the $N$-body problem in AdS at large spin $J$. We find that for the majority of states the effective quantum-mechanical problem becomes semiclassical with $\hbar=1/J$. The classical system at $J=\infty$ has $N-2$ degrees of freedom, and the classical phase space is identified with the positive Grassmannian $\mathrm{Gr}_{+}(2,N)$. The quantum problem is recovered via a Berezin-Toeplitz quantization of a classical Hamiltonian, which we describe explicitly. For $N=3$ the classical system has one degree of freedom and a detailed structure of the spectrum can be obtained from Bohr-Sommerfeld conditions. For all $N$, we show that the lowest excited states are approximated by a harmonic oscillator and find explicit expressions for their energies.
- [18] arXiv:2501.00092 (替换) [中文pdf, pdf, html, 其他]
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标题： 重CFT关联函数的矩和鞍点标题： Moments and saddles of heavy CFT correlators评论： 51页，4张图；第4版：已更新以匹配JHEP版本期刊参考： J. 高能物理 2025, 100 (2025)主题： 高能物理 - 理论 (hep-th) ; 统计力学 (cond-mat.stat-mech) ; 数学物理 (math-ph)
我们研究在共形四点关联函数中相同标量的算子乘积展开（OPE）作为Stieltjes矩问题，并使用Riemann-Liouville型分数微分算子从关联函数生成经典矩。 我们利用交叉对称性在大外部标度维数的“重”极限下推导出$\Delta$和$J_2 \equiv \ell(\ell+d-2)$中矩之间的主导和次主导关系，并结合单位性约束得出$\Delta$中矩序列的双侧界限以及$\Delta$和$J_2$之间的协方差。 满足这些界限的矩序列产生“鞍点”解，这些解被识别为广义自由场（GFF）理论中关联函数的特定极限。 这促使我们通过鞍点分析研究重GFF四点关联函数的扰动，并表明OPE中的鞍点来源于由高自旋共形块分解编码的固定长度算符族的贡献。 为了应用我们的技术，我们考虑由体相互作用扰动的四个相同单标量场的全息关联函数，并利用它们的前几个矩推导出高斯权重插值函数，这些函数预测了在重极限下相互作用双扭 operator 的OPE系数。
We study the operator product expansion (OPE) of identical scalars in a conformal four-point correlator as a Stieltjes moment problem, and use Riemann-Liouville type fractional differential operators to generate classical moments from the correlation function. We use crossing symmetry to derive leading and subleading relations between moments in $\Delta$ and $J_2 \equiv \ell(\ell+d-2)$ in the ``heavy" limit of large external scaling dimension, and combine them with constraints from unitarity to derive two-sided bounds on moment sequences in $\Delta$ and the covariance between $\Delta$ and $J_2$. The moment sequences which saturate these bounds produce ``saddle point" solutions to the crossing equations which we identify as particular limits of correlators in a generalized free field (GFF) theory. This motivates us to study perturbations of heavy GFF four-point correlators by way of saddle point analysis, and we show that saddles in the OPE arise from contributions of fixed-length operator families encoded by a decomposition into higher-spin conformal blocks. To apply our techniques, we consider holographic correlators of four identical single scalar fields perturbed by a bulk interaction, and use their first few moments to derive Gaussian weight-interpolating functions that predict the OPE coefficients of interacting double-twist operators in the heavy limit.
- [19] arXiv:2501.03481 (替换) [中文pdf, pdf, html, 其他]
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标题： 呼吸气体和非零背景下的聚焦非线性薛定谔方程的保护气标题： Breather gas and shielding for the focusing nonlinear Schrödinger equation with nonzero backgrounds评论： 21页，2图（将发表在《数学物理通讯》上）主题： 精确可解与可积系统 (nlin.SI) ; 数学物理 (math-ph) ; 模式形成与孤子 (nlin.PS) ; 光学 (physics.optics)
呼吸波在许多物理系统中被实验和理论上发现——特别是可积的非线性波模型中。一个相关问题是研究\textit{呼吸气体}，它是当$N\rightarrow \infty $时$N$-呼吸波解的极限。在本文中，我们研究了在非零边界条件下的聚焦非线性薛定谔（NLS）方程框架中的呼吸波气体，使用逆散射变换和黎曼-希尔伯特问题。我们研究了以$N$-呼吸波解形式出现的聚集态，当相应的离散谱集中在特定区域时。我们表明，呼吸波气体凝聚成一个单呼吸波解，其谱特征值位于圆域的中心，以及高阶求积域的多呼吸波解。呼吸波气体中的这些凝聚现象称为\textit{呼吸屏蔽}。特别地，当非零边界条件消失时，呼吸波气体简化为$n$-孤子解。当离散特征值集中在一条线上时，我们推导出相应的黎曼-希尔伯特问题。当离散谱在椭圆内均匀分布时，这等价于线域的情况。这些结果可能有助于在物理环境中设计呼吸波实验。
Breathers have been experimentally and theoretically found in many physical systems -- in particular, in integrable nonlinear-wave models. A relevant problem is to study the \textit{breather gas}, which is the limit, for $N\rightarrow \infty $, of $N$-breather solutions. In this paper, we investigate the breather gas in the framework of the focusing nonlinear Schr\"{o}dinger (NLS) equation with nonzero boundary conditions, using the inverse scattering transform and Riemann-Hilbert problem. We address aggregate states in the form of $N$-breather solutions, when the respective discrete spectra are concentrated in specific domains. We show that the breather gas coagulates into a single-breather solution whose spectral eigenvalue is located at the center of the circle domain, and a multi-breather solution for the higher-degree quadrature concentration domain. These coagulation phenomena in the breather gas are called \textit{breather shielding}. In particular, when the nonzero boundary conditions vanish, the breather gas reduces to an $n$-soliton solution. When the discrete eigenvalues are concentrated on a line, we derive the corresponding Riemann-Hilbert problem. When the discrete spectrum is uniformly distributed within an ellipse, it is equivalent to the case of the line domain. These results may be useful to design experiments with breathers in physical settings.
- [20] arXiv:2503.12423 (替换) [中文pdf, pdf, 其他]
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标题： 通过变换光学实现高阶奇异点的拓扑工程标题： Topological Engineering of High-Order Exceptional Points through Transformation Optics评论： 正文 - 5 图表期刊参考： 激光与光子学评论，e00593（2025）主题： 光学 (physics.optics) ; 数学物理 (math-ph)
非厄米光子系统中的异常点（EPs）由于其奇异的本征值拓扑结构和相关的异常物理现象，引起了广泛的研究兴趣。 这些特性使得从增强的量子计量学到手性光-物质相互作用等多种应用成为可能。 然而，在光学平台上实现高阶EPs仍然面临根本性的挑战，需要精确的多参数控制，这通常超出了传统设计能力。 本工作提出了一种通过变换光学（TO）原理工程高阶EPs的新框架，建立了数学奇点与可物理控制参数之间的直接对应关系。 我们的基于TO的范式解决了传统哈密顿量方法中的关键限制，其中抽象的参数空间缺乏与实验上可访问自由度的明确联系，同时提供了完整的场模解。 与现有的宇称-时间对称架构不同，我们的方法消除了EP设计中的对称性约束，显著扩展了非厄米光子工程的可能性。 所提出的技术实现了对纳米光子系统中EP形成和演化的前所未有的控制，为开发具有增强功能和鲁棒性的拓扑光学器件提供了新途径。
Exceptional points (EPs) in non-Hermitian photonic systems have attracted considerable research interest due to their singular eigenvalue topology and associated anomalous physical phenomena. These properties enable diverse applications ranging from enhanced quantum metrology to chiral light-matter interactions. Practical implementation of high order EPs in optical platforms however remains fundamentally challenging, requiring precise multi-parameter control that often exceeds conventional design capabilities. This work presents a novel framework for engineering high order EPs through transformation optics (TO) principles, establishing a direct correspondence between mathematical singularities and physically controllable parameters. Our TO-based paradigm addresses critical limitations in conventional Hamiltonian approaches, where abstract parameter spaces lack explicit connections to experimentally accessible degrees of freedom, while simultaneously providing full-field mode solutions. In contrast to prevailing parity-time-symmetric architectures, our methodology eliminates symmetry constraints in EP design, significantly expanding the possibilities in non-Hermitian photonic engineering. The proposed technique enables unprecedented control over EP formation and evolution in nanophotonic systems, offering new pathways for developing topological optical devices with enhanced functionality and robustness.
- [21] arXiv:2504.08062 (替换) [中文pdf, pdf, html, 其他]
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标题： 从热力学气体到指数膨胀的宇宙 - 芬斯勒-弗里德曼方程标题： From kinetic gases to an exponentially expanding universe - The Finsler-Friedmann equation期刊参考： JCAP10(2025)050主题： 广义相对论与量子宇宙学 (gr-qc) ; 宇宙学与非星系天体物理学 (astro-ph.CO) ; 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph)
我们研究了动力气体的引力场，超越了其通常从单粒子分布函数（1PDF）的二阶矩导出的常规方法，该方法作为爱因斯坦方程中的能量动量张量。这种标准方法引发了这样一个问题：为什么1PDF的其他矩（这些矩对于完全表征气体的动力学特性是必需的）不贡献于引力场，它们在解决暗能量问题中的可能相关性是什么？通过使用整个1PDF与芬斯勒时空几何的规范耦合，利用芬斯勒引力方程，我们表明这些高阶矩会非平凡地做出贡献。对我们的宇宙的芬斯勒几何描述使我们不仅能动态地确定标度因子，还能确定因果结构。我们发现，即使是一个芬斯勒真空解自然地允许一个指数膨胀的宇宙，而无需宇宙常数或任何额外的量。该解具有一个因果结构，它是弗里德曼-勒梅特-罗伯逊-沃尔克（FLRW）几何因果结构的轻微变形；在由宇宙时间定义的静止框架附近（即对于缓慢运动的物体），两种几何的因果结构几乎无法区分。
We investigate the gravitational field of a kinetic gas beyond its usual derivation from the second moment of the one-particle distribution function (1PDF), that serves as energy-momentum tensor in the Einstein equations. This standard procedure raises the question why the other moments of the 1PDF (which are needed to fully characterize the kinematical properties of the gas) do not contribute to the gravitational field and what could be their relevance in addressing the dark energy problem? Using the canonical coupling of the entire 1PDF to Finsler spacetime geometry via the Finsler gravity equation, we show that these higher moments contribute non-trivially. A Finslerian geometric description of our universe allows us to determine not only the scale factor but also of the causal structure dynamically. We find that already a Finslerian vacuum solution naturally permits an exponential expanding universe, without the need for a cosmological constant or any additional quantities. This solution possesses a causal structure which is a mild deformation of the causal structure of Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometry; close to the rest frame defined by cosmological time (i.e., for slowly moving objects), the causal structures of the two geometries are nearly indistinguishable.
- [22] arXiv:2505.05550 (替换) [中文pdf, pdf, html, 其他]
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标题： 平面费曼积分的非局部对称性标题： Non-Local Symmetries of Planar Feynman Integrals评论： 8页，v2：小幅度修改期刊参考： 物理评论快报 135, 151603 (2025)主题： 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph)
我们证明了在给定传播子幂次的某些约束条件下，任何平面拓扑的标量费曼图在杨振宁代数一级动量对称性下保持不变。 该证明依赖于将这种对称性与Bzowski、McFadden和Skenderis的共形单形的平面化版本相关联。 特别是，这证明了传播子幂次在动量空间中的位置空间共形条件的类比。 当与后者结合时，一级动量下的不变性意味着所考虑图的完整杨振宁对称性。 这些包括所有之前在示例层面已证明具有杨振宁对称性的标量费曼积分，例如鱼网图或织布机图，以及具有质量传播子的图的一般化。
We prove the invariance of scalar Feynman graphs of any planar topology under the Yangian level-one momentum symmetry given certain constraints on the propagator powers. The proof relies on relating this symmetry to a planarized version of the conformal simplices of Bzowski, McFadden and Skenderis. In particular, this proves a momentum-space analogue of the position-space conformal condition on propagator powers. When combined with the latter, the invariance under the level-one momentum implies full Yangian symmetry of the considered graphs. These include all scalar Feynman integrals for which a Yangian symmetry was previously demonstrated at the level of examples, e.g. the fishnet or loom graphs, as well as generalizations to graphs with massive propagators.
- [23] arXiv:2506.12249 (替换) [中文pdf, pdf, html, 其他]
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标题： 图论量子滤波系统标题： Graphon Quantum Filtering Systems主题： 概率 (math.PR) ; 数学物理 (math-ph) ; 组合数学 (math.CO) ; 量子物理 (quant-ph)
我们考虑一个具有平均场类型相互作用的不可交换量子粒子系统，该系统在密集图上受到连续测量的影响。 在平均场极限下，我们推导出一个基于图核的量子滤波系统，建立其适定性，并证明具有分块相互作用的多类玻色子系统的混沌传播。 然后我们讨论其在量子态制备和量子图核博弈中的应用。
We consider a non-exchangeable system of interacting quantum particles with mean-field type interactions, subject to continuous measurement on dense graphs. In the mean-field limit, we derive a graphon-based quantum filtering system, establish its well-posedness, and prove propagation of chaos for multi-class bosonic systems with blockwise interactions. We then discuss applications to quantum state preparation and quantum graphon games.
- [24] arXiv:2509.07423 (替换) [中文pdf, pdf, html, 其他]
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标题： 两星随机图的一组主变量标题： A set of master variables for the two-star random graph评论： v2：扩展版，已接受发表主题： 统计力学 (cond-mat.stat-mech) ; 无序系统与神经网络 (cond-mat.dis-nn) ; 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph) ; 概率 (math.PR)
两星随机图是具有非平凡边之间相互作用的最简单的指数随机图模型。 我们提出了一组辅助变量，用于控制当顶点数N趋于无穷大时的热力学极限。 这样的“主变量”在处理“大N”统计场论问题时通常非常受欢迎。 对于密集区域，当所有可能边的有限比例被填充时，此构造恢复了Park和Newman的平均场解，但对1/N修正有明确的控制。 我们利用这一优势计算了Park-Newman结果的第一个次主导修正，该修正包含了自由能的有限、非广延贡献。 对于具有有限平均度的稀疏区域，我们得到了Annibale-Courtney解的一个非常简洁的推导，该解最初是通过使用泛函积分开发的，在我们的处理中轻松避开了这一方法。
The two-star random graph is the simplest exponential random graph model with nontrivial interactions between the graph edges. We propose a set of auxiliary variables that control the thermodynamic limit where the number of vertices N tends to infinity. Such `master variables' are usually highly desirable in treatments of `large N' statistical field theory problems. For the dense regime when a finite fraction of all possible edges are filled, this construction recovers the mean-field solution of Park and Newman, but with an explicit control over the 1/N corrections. We use this advantage to compute the first subleading correction to the Park-Newman result, which encodes the finite, nonextensive contribution to the free energy. For the sparse regime with a finite mean degree, we obtain a very compact derivation of the Annibale-Courtney solution, originally developed with the use of functional integrals, which is comfortably bypassed in our treatment.
- [25] arXiv:2510.03090 (替换) [中文pdf, pdf, 其他]
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标题： 适用于CSS码的改进对数Sobolev不等式标题： Modified logarithmic Sobolev inequalities for CSS codesSebastian Stengele, Ángela Capel, Li Gao, Angelo Lucia, David Pérez-García, Antonio Pérez-Hernández, Cambyse Rouzé, Simone Warzel评论： 48页，7图 v2：修正了参考文献主题： 量子物理 (quant-ph) ; 数学物理 (math-ph)
我们考虑用于D维平移不变Calderbank-Shor-Steane (CSS)码的热化建模的Davies量子半群类。 我们证明了关于量子Gibbs态的Dobrushin-Shlosman型条件可推导出一个修正的对数Sobolev不等式，其常数与系统的大小无关。 这是通过将Stroock、Zegarlinski、Martinelli和Olivieri在经典热化方面的部分结果推广到CSS量子设置中实现的。 这些结果特别表明，在任意正温度下，二维的拓扑码和三维的拓扑码的星形部分会迅速热化，这意味着这些模型会迅速丢失存储的量子信息。
We consider the class of Davies quantum semigroups modelling thermalization for translation-invariant Calderbank-Shor-Steane (CSS) codes in D dimensions. We prove that conditions of Dobrushin-Shlosman-type on the quantum Gibbs state imply a modified logarithmic Sobolev inequality with a constant that is uniform in the system's size. This is accomplished by generalizing parts of the classical results on thermalization by Stroock, Zegarlinski, Martinelli, and Olivieri to the CSS quantum setting. The results in particular imply the rapid thermalization at any positive temperature of the toric code in 2D and the star part of the toric code in 3D, implying a rapid loss of stored quantum information for these models.
- [26] arXiv:2510.12853 (替换) [中文pdf, pdf, 其他]
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标题： 偏振重建的扩散模型标题： Diffusion models for polarimetric reconstruction of circumstellar environmentsQuentin Villegas, Laurence Denneulin (LRE), Simon Prunet (LAGRANGE), André Ferrari (LAGRANGE), Nelly Pustelnik (Phys-ENS), Éric Thiébaut (CRAL), Julian Tachella (Phys-ENS, CNRS), Maud Langlois (CRAL)评论： en langue française. GRETSI 2025 -- XXXe Colloque sur le Traitement du Signal et des Images, août 2025, Strasbourg, France主题： 天体物理学的仪器与方法 (astro-ph.IM) ; 数学物理 (math-ph)
在本文中，我们提出了一种结合扩散模型和反问题的方法，用于原恒星盘图像的重建。 我们的方法建立在偏振成像的Rhapsodie框架之上，将其经典先验替换为在合成数据上训练的扩散模型。 我们的公式明确包含了恒星泄漏，同时高效处理高对比度偏振成像固有的缺失数据和高水平噪声。 实验表明，在我们的假设框架内，与传统方法相比有显著改进，为研究原恒星环境开辟了新的前景。
In this paper, we propose an approach combining diffusion models and inverse problems for the reconstruction of circumstellar disk images. Our method builds upon the Rhapsodie framework for polarimetric imaging, substituting its classical prior with a diffusion model trained on synthetic data. Our formulation explicitly incorporates stellar leakage while efficiently handling missing data and high level noise inherent to high-contrast polarimetric imaging. Experiments show significant improvement over conventional methods within our framework of assumptions, opening new perspectives for studying circumstellar environments.