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[1] arXiv:2508.21108 [中文pdf, pdf, html, 其他]

标题： S_n的混合对称性：U(d)子矩阵采样中的不可约表示函数 显示英文标题

标题： Mixed symmetries of S_n: immanants in the sampling of U(d) submatrices

Jacob Daigle, Hubert de Guise, Trevor Welsh

评论： 10页

主题： 数学物理 (math-ph) ; 表示理论 (math.RT)

我们提供关于Haar分布酉矩阵集合的子矩阵的不可约量的均值和高阶矩的结果，大部分没有证明。 本文基于Trevor Welsh于2025年7月在布拉格举行的ISQS29会议上所做的报告。 显示英文摘要

We provide results on the mean and higher moments of immanants of submatrices of ensembles of Haar-distributed unitary matrices, mostly without proofs. This paper is based on a talk presented at ISQS29 in Prague in July 2025 by Trevor Welsh.

[2] arXiv:2508.21215 [中文pdf, pdf, html, 其他]

标题： 随机聚合物模型的特征值统计：局域化与非局域化 显示英文标题

标题： Eigenvalue statistics for random polymer models: Localization and delocalization

Peter D. Hislop, Fumihiko Nakano

主题： 数学物理 (math-ph)

我们研究与一维格子随机聚合物模型相关的局部特征值统计（LES）。 我们考虑由两种聚合物构成的模型。 每种聚合物是一个有限区间的格点，具有有限势。 这些聚合物沿$\mathbb{Z}$按照伯努利分布分布。 这些模型的确定性谱是密集的纯点谱，并且已知包含有限多个临界能量。 在本文中，我们证明在这些临界能量处的 LES 由均匀钟过程描述，而在确定性谱中任何其他能量处的展开特征值的 LES 是泊松点过程。 这些结果增强了我们对这些模型的理解，这些模型在避开临界能量的任何能量区间内表现出动力学局域化 [Damanik, Sims, Stolz] [De Bievre, Germinet]，以及在初始状态支持于整数点的波包中表现出非平凡输运 [Jitomirskaya, Schultz-Baldes, Stolz]。 我们表明，这些初始状态在包含所有临界能量的能量区间的谱子空间上的投影表现出非平凡输运，从而细化了非平凡输运与临界能量之间的联系。 最后，我们还证明在展开的 LES 中，临界能量处的转变是尖锐的。 显示英文摘要

We study the local eigenvalue statistics (LES) associated with one-dimensional lattice models of random polymers. We consider models constructed from two polymers. Each polymer is a finite interval of lattice points with a finite potential. These polymers are distributed along $\mathbb{Z}$ according to a Bernoulli distribution. The deterministic spectrum for these models is dense pure point, and is known to contain finitely-many critical energies. In this paper, we prove that the LES centered at these critical energies is described by a uniform clock process, and that the LES for the unfolded eigenvalues, centered at any other energy in the deterministic spectrum, is a Poisson point process. These results add to our understanding of these models that exhibit dynamical localization in any energy interval avoiding the critical energies [Damanik, Sims, Stolz] [De Bievre, Germinet], and nontrivial transport for wave packets with initial states supported at an integer point [Jitomirskaya, Schultz-Baldes, Stolz]. We show that the projection of these initial states onto spectral subspaces associated with any energy interval that contains all of the critical energies exhibit nontrivial transport, refining the connection between nontrivial transport and the critical energies. Finally, we also prove that the transition in the unfolded LES is sharp at the critical energies.

[3] arXiv:2508.21349 [中文pdf, pdf, html, 其他]

标题： 高温下的矩阵调和分析通过狄利克雷过程 显示英文标题

标题： Matrix harmonic analysis at high temperature via the Dirichlet process

Jiyuan Zhang

主题： 数学物理 (math-ph) ; 概率 (math.PR)

我们研究大尺寸随机矩阵的调和分析，其Dyson指数同时趋于零，即在高温极限下。在此情况下，极限经验谱分布以及经验谱分布的多元Bessel函数/Heckman-Opdam超几何函数与Markov-Krein对应关系密切相关。利用Dirichlet过程理论研究了Markov-Krein对应关系的唯一性、存在性及其他性质。 显示英文摘要

We investigate harmonic analysis of random matrices of large size with their Dyson indices going simultaneous to zero, that is in the high temperature limit. In this regime, the limiting empirical spectral distribution and the multivariate Bessel function/Heckman-Opdam hypergeometric function of the empirical spectral distribution are intimately related to the Markov-Krein correspondence. The uniqueness, existence and other properties of the Markov-Krein correspondence are studied using the theory of the Dirichlet process.

[4] arXiv:2508.21409 [中文pdf, pdf, html, 其他]

标题： 退火Potts模型中确定临界逆温度的量的分析，具有帕累托顶点权重 显示英文标题

标题： Analysis of quantities determining the critical inverse temperature in the annealed Potts model with Pareto vertex weights

A.J.E.M. Janssen

主题： 数学物理 (math-ph) ; 概率 (math.PR)

我们在此工作中考虑了关键量$t_c$，它决定了稀疏秩-1随机图上的$q$-状态 Potts 模型的临界逆温度$\beta_c$，其中顶点配备了帕累托权重密度$(\tau-1)\,w^{-\tau}\,{\cal X}_{[1,\infty)}(w)$。 在\cite{ref1}中显示，这个$t_c$是由适当组合平稳性条件和外部场$B$等于 0 的临界性条件得到的函数${\cal K}$的唯一正零点，并且$q\geq3$和$\tau\geq4$，见\cite{ref1}，定理~1.14 和定理~1.21 以及它们在\cite{ref1}，第~7.1 节和第~7.3 节中的证明。 从\cite{ref1}的证明中可以看出，${\cal K}'$和${\cal K}''$也分别有一个唯一的正零点，$t_c'$和$t_c''$，以及$t_c'=t_b$和$t_c''=t_{\ast}$，其中$t_b$和$t_{\ast}$分别是${\cal F}_0(t)-t\,{\cal F}_0'(t)$和${\cal F}_0''(t)$的唯一正零点。 这里，${\cal F}_0(t)=E\,[W(e^{tW}-1)/(E\,[W]\,(e^{tW}+q-1))]$，和$t_c$，$t_b$和$t_{\ast}$在\cite{ref1}的图形分析中起关键作用，第5.1节和图1。 此外，$\gamma_c=\exp(\beta_c)-1$和$t_c$根据$\gamma_c=t_c/{\cal F}_0(t_c)$相关。 我们分析一般实数$t_c$、$t_c'$和$t_c''$以及它们的定义方程${\cal K}(t_c)={\cal K}'(t_c')={\cal K}''(t_c'')=0$的适当表述，针对一般的实数$\tau\geq4$和一般的实数$q>2$。 因此，我们除了不等式$0<t_c''<t_c'<t_c<\infty$外，还找到了简单的上界$t_c<2\,{\rm ln}(q-1)$，$t_c'<\frac32\,{\rm ln}(q-1)$，$t_c''<{\rm ln}(q-1)$，以及这些简单界的一些改进形式，以及关于$q$的大值行为的相应结果，以及$t_c$，$t_c$和$t_c''$的相应结果。 我们证明这些界限是精确的，因为在极限齐次情况下它们成立等式$\tau\to\infty$。 显示英文摘要

We consider in this work the crucial quantity $t_c$ that determines the critical inverse temperature $\beta_c$ in the $q$-state Potts model on sparse rank-1 random graphs where the vertices are equipped with a Pareto weight density $(\tau-1)\,w^{-\tau}\,{\cal X}_{[1,\infty)}(w)$. It is shown in \cite{ref1} that this $t_c$ is the unique positive zero of a function ${\cal K}$ that is obtained by an appropriate combination of the stationarity condition and the criticality condition for the case the external field $B$ equals 0 and that $q\geq3$ and $\tau\geq4$, see \cite{ref1}, Theorem~1.14 and Theorem ~1.21 and their proofs in \cite{ref1}, Section~7.1 and Section~7.3. From the proof of \cite{ref1}, Theorem~1.14, it is seen that ${\cal K}'$ and ${\cal K}''$ also have a unique positive zero, $t_c'$ and $t_c''$, respectively, and $t_c'=t_b$ and $t_c''=t_{\ast}$, where $t_b$ and $t_{\ast}$ are the unique positive zeros of ${\cal F}_0(t)-t\,{\cal F}_0'(t)$ and ${\cal F}_0''(t)$, respectively. Here, ${\cal F}_0(t)=E\,[W(e^{tW}-1)/(E\,[W]\,(e^{tW}+q-1))]$, and $t_c$, $t_b$ and $t_{\ast}$ play a key role in the graphical analysis of \cite{ref1}, Section~5.1 and Figure~1. Furthermore, $\gamma_c=\exp(\beta_c)-1$ and $t_c$ are related according to $\gamma_c=t_c/{\cal F}_0(t_c)$. We analyse $t_c$, $t_c'$ and $t_c''$ for general real $\tau\geq4$ and general real $q>2$ by an appropriate formulation of their defining equations ${\cal K}(t_c)={\cal K}'(t_c')={\cal K}''(t_c'')=0$. Thus we find, along with the inequality $0<t_c''<t_c'<t_c<\infty$, the simple upper bounds $t_c<2\,{\rm ln}(q-1)$, $t_c'<\frac32\,{\rm ln}(q-1)$, $t_c''<{\rm ln}(q-1)$, as well as certain sharpenings of these simple bounds and counterparts about the large-$q$ behaviour of $t_c$, $t_c$ and $t_c''$. We show that these bounds are sharp in the sense that they hold with equality for the limiting homogeneous case $\tau\to\infty$.

[5] arXiv:2508.21483 [中文pdf, pdf, html, 其他]

标题： 有限的$N$矩阵自由累积量的前驱 显示英文标题

标题： Finite $N$ precursors of the free cumulants

Sylvain Lacroix, Jean-Bernard Zuber

评论： 48页，1图

主题： 数学物理 (math-ph) ; 高能物理 - 理论 (hep-th) ; 组合数学 (math.CO) ; 概率 (math.PR)

We introduce $\mathrm{U}(N)$ invariant polynomials on the space of $N\times N$ matrices that are precursors of free cumulants in various respects. First, they are polynomials of deterministic matrices, that are not yet evaluated over some probability law, contrary to what is usually meant by cumulants. Secondly, they converge towards the algebraic expression of free cumulants in terms of moments as $N\to \infty$, with $1/N^2$ corrections expressed in terms of monotone Hurwitz numbers. Their most crucial property is their additivity with respect to averaging over sums of $\mathrm{U}(N)$ conjugacy orbits, providing a finite $N$ version of the well-known additivity of free cumulants in free probability. Finally, they extend several properties of free cumulants at finite $N$, including a Wick rule for their average over a Gaussian weight and their appearance in various matrix integrals. 基于这些前驱的可加性性质，我们还定义并计算了一个余乘法，描述了一般不变多项式在添加$\mathrm{U}(N)$共轭轨道时的行为，以及它们在$\mathrm{U}(N)$-不变随机矩阵之和上的期望值。在我们的构造中，所谓的HCIZ积分起着核心作用，既用于前驱的定义，也用于其性质的推导。 显示英文摘要

We introduce $\mathrm{U}(N)$ invariant polynomials on the space of $N\times N$ matrices that are precursors of free cumulants in various respects. First, they are polynomials of deterministic matrices, that are not yet evaluated over some probability law, contrary to what is usually meant by cumulants. Secondly, they converge towards the algebraic expression of free cumulants in terms of moments as $N\to \infty$, with $1/N^2$ corrections expressed in terms of monotone Hurwitz numbers. Their most crucial property is their additivity with respect to averaging over sums of $\mathrm{U}(N)$ conjugacy orbits, providing a finite $N$ version of the well-known additivity of free cumulants in free probability. Finally, they extend several properties of free cumulants at finite $N$, including a Wick rule for their average over a Gaussian weight and their appearance in various matrix integrals. Building on the additivity property of these precursors, we also define and compute a coproduct describing the behaviour of general invariant polynomials with respect to the addition of $\mathrm{U}(N)$ conjugacy orbits, as well as their expectation values on sums of $\mathrm{U}(N)$-invariant random matrices. In our construction, a central role is played by the so-called HCIZ integral, both for the definition of the precursors and for the derivation of their properties.

[6] arXiv:2508.21502 [中文pdf, pdf, 其他]

标题： 费米物质与 $\mathbb{Z}_2$-规范场耦合的 $π$-通量相中的任意子 显示英文标题

标题： Anyons in the $π$-flux phase of fermionic matter coupled to a $\mathbb{Z}_2$-gauge field

Sven Bachmann, Leonardo Goller, Marcello Porta

评论： 54页，21图

主题： 数学物理 (math-ph)

我们考虑一个由弱相互作用的具有自旋的格点费米子与动态的$\mathbb{Z}_2$规范场耦合的系统。 基态位于每个晶胞上均匀的$\pi$通量的区域，单极子是大质量的。 在费米子存在交替质量的情况下，这在大环面上产生了一个完全禁带的四维基态空间。 它是拓扑有序的。 通过考虑绝热的$\pi$通量插入，我们构造了带有色散的单极子激发，并表明它们与费米子激发的编织行为与表面码相同。 显示英文摘要

We consider a system of weakly interacting spinful lattice fermions coupled to a dynamical $\mathbb{Z}_2$ gauge field. The ground state lies in the sector of a uniform $\pi$-flux per plaquette and the monopoles are massive. In the presence of a staggered mass for the fermions, this yields a fully gapped, four-dimensional ground state space on large tori. It is topologically ordered. By considering adiabatic $\pi$-flux insertion, we construct dressed monopole excitations and show that their braiding with the fermionic excitations are those of the toric code.

[7] arXiv:2508.21588 [中文pdf, pdf, html, 其他]

标题： 赫尔格洛茨形式主义，艾森哈特提升和基灵向量 显示英文标题

标题： Herglotz's formalism, Eisenhart lift and Killing vectors

Krystian Bartczak, Piotr Kosiński

评论： 19页，无图

主题： 数学物理 (math-ph)

Eisenhart提升被扩展到由作用依赖拉格朗日量描述的动力学。 结果得到的Brinkmann度规依赖于所有坐标。 证明了初始动力学的对称性导致Brinkmann度规存在（共形）Killing向量。 给出了等效的时间和作用依赖描述的例子，这些描述导致共形等价的度规。 显示英文摘要

The Eisenhart lift is extended to the dynamics described by action-dependent Lagrangians. The resulting Brinkmann metrics depends on all coordinates. It is shown that the symmetries of the initial dynamics result in the existence of (conformal) Killing vectors of Brinkmann metric. An example is given of equivalent time- and action-dependent descriptions which result in conformally equivalent metrics.

交叉提交 (展示 12 之 12 条目 )

[8] arXiv:2508.21276 (交叉列表自 hep-th) [中文pdf, pdf, html, 其他]

标题： 量子场论中的有限熵和 显示英文标题

标题： Finite entropy sums in quantum field theory

Mark Van Raamsdonk

评论： 29页，5图

主题： 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph) ; 量子物理 (quant-ph)

与传统局部量子场论中空间子系统相关的熵通常在空间区域具有边界时发散。 然而，在各种子系统的熵的某些线性组合中，这些发散可能相互抵消，从而得到提供关于底层状态的信息理论数据的有限量。 在本说明中，我们表明所有此类量都可以写成三种基本类型量的线性组合：i) 一个空间子系统的熵减去其补子系统的熵，ii) 非相邻子系统之间的互信息，以及iii) 不相交子系统三元组的三重信息。 对于空间切片的一个固定区域分解，我们描述了一组熵的和的基，这些和的熵对于这些区域的集合而言，所有与区域边界以及区域更高余维交叉相关的发散都会被抵消。 本工作中使用的关键数学技术（布尔立方体上的傅里叶变换和偏序集上函数的莫比乌斯变换）以及几个主要的证明思路是由AI（ChatGPT5）提出的。 我们根据我们的经验，对AI在物理学和数学中的使用提出了一些评论。 显示英文摘要

Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems, these divergences may cancel, giving finite quantities that provide information-theoretic data about the underlying state. In this note, we show that all such quantities can be written as linear combinations of three basic types of quantities: i) the entropy of a spatial subsystem minus the entropy of its complementary subsystem, ii) the mutual information between non-adjacent subsystems, and iii) the tripartite information for triples of disjoint sub-systems. For a fixed decomposition of a spatial slice into regions, we describe a basis of sums of entropies for collections of for these regions for which all divergences related to both region boundaries and higher-codimension intersections of regions cancel. Key mathematical technology used in this work (Fourier transforms on the Boolean cube and M\"obius transformations of functions on partially ordered sets) and several of the main proof ideas were suggested by AI (ChatGPT5). We offer a few comments on the use of AI in physics and mathematics, based on our experience.

[9] arXiv:2508.21288 (交叉列表自 quant-ph) [中文pdf, pdf, html, 其他]

标题： 使用加权模型计数的量子物理 显示英文标题

标题： Quantum Physics using Weighted Model Counting

Dirck van den Ende, Joon Hyung Lee, Alfons Laarman

主题： 量子物理 (quant-ph) ; 统计力学 (cond-mat.stat-mech) ; 数学物理 (math-ph)

加权模型计数（WMC）已被证明在计算机科学、物理学等领域的一系列任务中非常有效。 然而，现有的在量子物理中使用WMC的方法仅针对特定问题实例，缺乏一种通用框架来使用WMC表达问题。 这限制了这些方法在其他应用中的可重用性，并可能导致每个实例的数学严谨性不足。 我们提出了一种将线性代数问题（特别是物理学和量子计算中的问题）表达为WMC实例的方法。 我们通过引入一种将狄拉克符号转换为WMC问题的框架来实现这一点。 我们通过类型系统和语义学理论构建了这个框架，并在Python中提供了实现。 我们展示了我们的框架在计算几个物理模型的分区函数中的有效性：横场伊辛模型（量子）和庞茨模型（经典）。 结果表明，通过我们的框架，自动化推理中开发的启发式方法可以系统地应用于量子物理中的广泛问题类别。 显示英文摘要

Weighted model counting (WMC) has proven effective at a range of tasks within computer science, physics, and beyond. However, existing approaches for using WMC in quantum physics only target specific problem instances, lacking a general framework for expressing problems using WMC. This limits the reusability of these approaches in other applications and risks a lack of mathematical rigor on a per-instance basis. We present an approach for expressing linear algebraic problems, specifically those present in physics and quantum computing, as WMC instances. We do this by introducing a framework that converts Dirac notation to WMC problems. We build up this framework theoretically, using a type system and denotational semantics, and provide an implementation in Python. We demonstrate the effectiveness of our framework in calculating the partition functions of several physical models: The transverse-field Ising model (quantum) and the Potts model (classical). The results suggest that heuristics developed in automated reasoning can be systematically applied to a wide class of problems in quantum physics through our framework.

[10] arXiv:2508.21348 (交叉列表自 quant-ph) [中文pdf, pdf, html, 其他]

标题： $k$-正映射：新的特征描述和生成方法 显示英文标题

标题： $k$-Positive Maps: New Characterizations and a Generation Method

Frederik vom Ende, Sumeet Khatri, Sergey Denisov

评论： 18+8页，作为“量子力学中的数学结构2”会议论文集提交给《开放系统与信息动力学》

主题： 量子物理 (quant-ph) ; 数学物理 (math-ph) ; 环与代数 (math.RA)

我们研究矩阵代数上的$k$-正线性映射并解决两个问题，(i)$k$-正性的表征和(ii)非可分解$k$-正映射的生成。 在表征方面，我们推导出与$k$-正性等价的基于优化的条件，(a)当$k=d$时简化为一个简单的检查，(b)揭示了与某些三阶张量谱范数的直接联系（与已知的$k<d$的NP难性障碍一致），以及(c)将$k$-正性重新表述为关于可分离态的新优化问题，从而明确地将其与可分离性测试联系起来。 在生成方面，我们引入了一种基于李-半群的方法，该方法从一个单一的$k$正映射开始，生成保持$k$正性和不可分解性的小时间参数族。我们通过为$d=3$和$d=4$生成这样的族来说明这一点。我们还制定了一种半定规划（SDP）来测试正偏转转置（PPT）平方猜想的一种等价形式（并且没有发现后者有任何违反情况）。我们的结果提供了认证$k$正性的实用计算工具，并提供了一种系统的方法来采样$k$正性的不可分解映射。 显示英文摘要

We study $k$-positive linear maps on matrix algebras and address two problems, (i) characterizations of $k$-positivity and (ii) generation of non-decomposable $k$-positive maps. On the characterization side, we derive optimization-based conditions equivalent to $k$-positivity that (a) reduce to a simple check when $k=d$, (b) reveal a direct link to the spectral norm of certain order-3 tensors (aligning with known NP-hardness barriers for $k<d$), and (c) recast $k$-positivity as a novel optimization problem over separable states, thereby connecting it explicitly to separability testing. On the generation side, we introduce a Lie-semigroup-based method that, starting from a single $k$-positive map, produces one-parameter families that remain $k$-positive and non-decomposable for small enough times. We illustrate this by generating such families for $d=3$ and $d=4$. We also formulate a semi-definite program (SDP) to test an equivalent form of the positive partial transpose (PPT) square conjecture (and do not find any violation of the latter). Our results provide practical computational tools for certifying $k$-positivity and a systematic way to sample $k$-positive non-decomposable maps.

[11] arXiv:2508.21427 (交叉列表自 math.NA) [中文pdf, pdf, html, 其他]

标题： 计算超相对论欧拉方程的径向对称解的熵稳定不连续伽辽金方法 显示英文标题

标题： Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods

Ferdinand Thein, Hendrik Ranocha

主题： 数值分析 (math.NA) ; 数学物理 (math-ph)

超相对论欧拉方程描述了在热能占主导地位的相对论情况下的气体。 对于理想气体，这些方程是用压力、无量纲四速度的空间部分和粒子密度来表示的。 Kunik 等人（2024，https://doi.org/10.1016/j.jcp.2024.113330）为超相对论欧拉方程提出了真正的多维基准问题。 特别是，他们将径向对称问题的全二维不连续伽辽金模拟与使用特定一维方案计算的解进行了比较。 解中特别值得关注的是激波的形成和压力爆炸。 在本工作中，我们推导了超相对论欧拉方程的熵稳定通量。 因此，我们推导了主场（或熵变量）及其相应的势能。 然后，我们提出熵稳定通量，并以不同测试案例的二维和三维模拟结果结束。 显示英文摘要

The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressure, the spatial part of the dimensionless four-velocity, and the particle density. Kunik et al.\ (2024, https://doi.org/10.1016/j.jcp.2024.113330) proposed genuine multi--dimensional benchmark problems for the ultra--relativistic Euler equations. In particular, they compared full two-dimensional discontinuous Galerkin simulations for radially symmetric problems with solutions computed using a specific one-dimensional scheme. Of particular interest in the solutions are the formation of shock waves and a pressure blow-up. In the present work we derive an entropy-stable flux for the ultra--relativistic Euler equations. Therefore, we derive the main field (or entropy variables) and the corresponding potentials. We then present the entropy-stable flux and conclude with simulation results for different test cases both in 2D and in 3D.

[12] arXiv:2508.21464 (交叉列表自 math.AP) [中文pdf, pdf, 其他]

标题： 1D准解的2D Chern-Simons-Schr{ö}方程组 显示英文标题

标题： 1D quasi-solutions of the 2D Chern-Simons-Schr{ö}dinger system

Nicolas Rougerie (UMPA-ENSL), Qiyun Yang (UMPA-ENSL)

主题： 偏微分方程分析 (math.AP) ; 中尺度与纳米尺度物理 (cond-mat.mes-hall) ; 量子气体 (cond-mat.quant-gas) ; 数学物理 (math-ph)

我们研究一个二维阿贝尔任意子系统的平均场模型，该模型由薛定谔物质场与陈-西蒙斯规范场的动态耦合给出。 我们通过添加一个强各向异性的捕获势（波导）作用于薛定谔场，并对紧密约束方向进行积分，推导出一个有效的1D方程。 波导松散方向的有效动力学被证明由经典的1D五次NLS方程支配。 显示英文摘要

We study a mean-field model for a system of 2D abelian anyons, given by the dynamics of a Schr{\"o}dinger matter field coupled to a Chern-Simons gauge field. We derive an effective 1D equation by adding a strongly anisotropic trapping potential (wave-guide) acting on the Schr{\"o}dinger field, and tracing out the tight confinement direction. The effective dynamics in the loose direction of the wave-guide turns out to be governed by the classical 1D quintic NLS equation.

[13] arXiv:2508.21525 (交叉列表自 physics.flu-dyn) [中文pdf, pdf, html, 其他]

标题： 莫法特-普克纳切夫流：一个旧问题的新转折 显示英文标题

标题： The Moffatt-Pukhnachev flow: a new twist on an old problem

Antonio J. Bárcenas-Luque, Mark G. Blyth

主题： 流体动力学 (physics.flu-dyn) ; 数学物理 (math-ph)

在水平圆柱体外表面，其角速度为具有指定频率和振幅的周期性时间变化的情况下，研究了薄粘性薄膜的流动。 恒定角速度问题最初由Moffatt（1977）和Pukhnachev（1977）研究。 忽略表面张力。 在一定范围的振荡振幅和频率下，求解了膜厚度的演化方程。 一个在振幅-频率空间中绘制的爆裂图显示了高度复杂的类似分形的结构，表现出自相似性。 对于一般的初始条件，薄膜表面在有限时间内达到斜率奇点并趋于翻转。 使用多尺度方法对高频和低频极限进行了渐近分析。 在高频情况下，分析表明，适当选择初始轮廓可以显著延迟翻转时间，甚至产生周期性时间解。 在低频极限下，如果振荡振幅低于临界值，可以构造一个不翻转的准周期解。 超过该值后，解不可避免地趋向于爆裂。 展示了如何与稳定旋转圆柱体问题共同构造出现单个冲击或双冲击的解。 显示英文摘要

The flow of a thin viscous film on the outside of a horizontal circular cylinder, whose angular velocity is time-periodic with specified frequency and amplitude, is investigated. The constant angular velocity problem was originally studied by Moffatt (1977) and Pukhnachev (1977). Surface tension is neglected. The evolution equation for the film thickness is solved numerically for a range of oscillation amplitudes and frequency. A blow-up map charted in amplitude-frequency space reveals highly intricate fractal-like structures exhibiting self-similarity. For a general initial condition the film surface reaches a slope singularity at a finite time and tends to overturn. The high-frequency and low-frequency limits are examined asymptotically using a multiple-scales approach. At high frequency the analysis suggests that an appropriate choice of initial profile can substantially delay the overturning time, and even yield a time-periodic solution. In the low-frequency limit it is possible to construct a quasi-periodic solution that does not overturn if the oscillation amplitude lies below a threshold value. Above this value the solution tends inexorably toward blow-up. It is shown how solutions exhibiting either a single-shock or a double-shock may be constructed in common with the steadily rotating cylinder problem.

[14] arXiv:2508.21528 (交叉列表自 quant-ph) [中文pdf, pdf, html, 其他]

标题： 分数量子力学中的量子阱 显示英文标题

标题： Quantum Well in Fractional Quantum Mechanics

Nick Laskin

评论： 10页

主题： 量子物理 (quant-ph) ; 数学物理 (math-ph)

在分数量子力学的框架下，已经找到了一个量子粒子被限制在量子阱中——一个对称的一维有限势阱的能量谱的精确解。 描述了一种简单的图形算法，用于获得量子阱中的离散能级数量及其相关的能量值。 所呈现的结果为使用量子阱模拟分数量子力学开辟了新的可能性。 显示英文摘要

Within the framework of fractional quantum mechanics, an exact solution has been found for the energy spectrum of a quantum particle confined in a quantum well - a symmetric one-dimensional finite potential well. A simple graphical algorithm is described for obtaining the number of discrete levels in a quantum well and their associated energy values. The presented results open up new possibilities for emulating fractional quantum mechanics using quantum wells.

[15] arXiv:2508.21590 (交叉列表自 hep-th) [中文pdf, pdf, html, 其他]

标题： 狄拉克粒子，自旋和光子 显示英文标题

标题： Dirac particles, spin and photons

Alexander D. Popov

评论： 56页

主题： 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph) ; 量子物理 (quant-ph)

我们用相空间$X=T^* R^{1,3}\times C^2_L\times C^2_R$中移动的点来描述自旋为相对论粒子，其中$T^* R^{1,3}=R^{1,3}\times R^{1,3}$是坐标和动量的空间，$C^2_L$和$C^2_R$是洛伦兹群类型$(\frac12 , 0)$和$(0, \frac12)$的表示空间。 从相对论力学中具有洛伦兹不变的哈密顿函数$H$在相空间$X$上过渡到量子力学中的哈密顿算子$\hat H$，我们引入了两个复共轭线丛$L_C^+$和$L_C^-$在$X$上。 量子粒子被引入为沿空间$C^2_L\times C^2_R$解析的丛$L_C^+$的截面$\Psi_+$，反粒子是沿内部自旋空间$C^2_L\times C^2_R$反解析的丛$L_C^-$的截面$\Psi_-^{}$。 The wave functions $\Psi_\pm$ are characterized by conserved charges $q_{\sf{v}}=\pm 1$ associated with the structure group U(1)$_{\sf{v}}$ of the bundles $L_C^\pm$. Wave functions $\Psi_\pm$ are governed by relativistic analogue of the Schrödinger equation. 我们展示如何从这些方程在自旋空间坐标$C^2_L\times C^2_R$中函数$\Psi_\pm^{}$的零阶、一阶和二阶展开中得到自旋$s=0$(Klein-Gordon)、自旋$s=\frac12$(Dirac) 和自旋$s=1$(Proca 场) 的场。 这些场的 Klein-Gordon、Dirac 和 Proca 方程来源于扩展相空间$T^* R^{1,3}\times C^2_L\times C^2_R$上的薛定谔方程。 利用这些结果，我们还引入描述第一量子化光子的方程。 我们证明，考虑场 $\Psi_\pm$ 的电荷 $q_{\sf{v}}=\pm 1$ 会改变内积和电流的定义，这消除了相对论量子力学中的负能和负概率。 显示英文摘要

We describe relativistic particles with spin as points moving in phase space $X=T^* R^{1,3}\times C^2_L\times C^2_R$, where $T^* R^{1,3}=R^{1,3}\times R^{1,3}$ is the space of coordinates and momenta, and $C^2_L$ and $C^2_R$ are the spaces of representation of the Lorentz group of type $(\frac12 , 0)$ and $(0, \frac12)$. Passing from relativistic mechanics with a Lorentz-invariant Hamiltonian function $H$ on the phase space $X$ to quantum mechanics with a Hamiltonian operator $\hat H$, we introduce two complex conjugate line bundles $L_C^+$ and $L_C^-$ over $X$. Quantum particles are introduced as sections $\Psi_+$ of the bundle $L_C^+$ holomorphic along the space $C^2_L\times C^2_R$, and antiparticles are sections $\Psi_-^{}$ of the bundle $L_C^-$ antiholomorphic along the internal spin space $C^2_L\times C^2_R$. The wave functions $\Psi_\pm$ are characterized by conserved charges $q_{\sf{v}}=\pm 1$ associated with the structure group U(1)$_{\sf{v}}$ of the bundles $L_C^\pm$. Wave functions $\Psi_\pm$ are governed by relativistic analogue of the Schr\"odinger equation. We show how fields with spin $s=0$ (Klein-Gordon), spin $s=\frac12$ (Dirac) and spin $s=1$ (Proca fields) arise from these equations in the zeroth, first, and second order expansions of the functions $\Psi_\pm^{}$ in the coordinates of the spin space $C^2_L\times C^2_R$. The Klein-Gordon, Dirac and Proca equations for these fields follow from the Schr\"odinger equation on the extended phase space $T^* R^{1,3}\times C^2_L\times C^2_R$. Using these results, we also introduce equations describing first quantized photons. We show that taking into account the charges $q_{\sf{v}}=\pm 1$ of the fields $\Psi_\pm$ changes the definitions of the inner products and currents, which eliminates negative energies and negative probabilities from relativistic quantum mechanics.

[16] arXiv:2508.21633 (交叉列表自 hep-th) [中文pdf, pdf, html, 其他]

标题： 三维共形场理论中的旋量和扭量形式主义讲座 显示英文标题

标题： Lectures on the Spinor and Twistor Formalism in 3D Conformal Field Theory

Dhruva K.S

评论： 54页+6页附录，55个练习

主题： 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph)

这些笔记基于我在2025年在IISER Bhopal举行的$\text{ST}^4$讲座的内容。 在这些笔记中，我们研究了旋量和扭量方法在三维共形场理论中的应用。 它们分为三部分，分别涉及旋量动量、扭量和超扭量。 在第一部分中，我们介绍了非定域旋量动量形式，并将其应用于多个上下文，包括双复制关系、与四维散射振幅的联系、Chern-Simons物质理论中的关联函数以及手性高自旋理论的全息对应。 笔记的第二部分介绍了扭量空间形式。 在讨论了扭量空间的几何之后，我们推导了守恒流、任意标度维度的标量以及一般非守恒算符的Penrose变换。 我们还明确展示了旋量和扭量方法之间的关系。 我们讨论了这些算符和守恒流的关联函数在扭量空间中显著简化，揭示了它们隐藏的简洁性。 我们还将我们的构造扩展到超共形场理论，并发展了一个显式的超扭量空间形式，并推导了超对称的Penrose变换。 我们发现超对称的关联函数是其非超对称对应物的简单且自然的推广。 这些笔记旨在自成体系，并包含超过$50$个练习来说明该形式。 显示英文摘要

These notes are based on my lectures given at $\text{ST}^4$ 2025 held at IISER Bhopal. We study the application of spinor and twistor methods to three dimensional conformal field theories in these notes. They are divided into three parts dealing with spinor helicity, twistors and super-twistors respectively. In the first part, we introduce the off-shell spinor helicity formalism and apply it in several contexts including double copy relations, connection to four dimensional scattering amplitudes, correlators in Chern-Simons matter theories and the holography of chiral higher spin theory. The second part of the notes introduces the twistor space formalism. After discussing the geometry of twistor space, we derive the Penrose transform for conserved currents, scalars with arbitrary scaling dimension as well as generic non-conserved operators. We also explicitly show how the spinor and twistor approaches are related. We discuss how correlators of these operators and conserved currents in particular drastically simplify in twistor space unveiling their hidden simplicity. We also extend our construction to super-conformal field theories and develop a manifest super-twistor space formalism and derive the supersymmetric Penrose transform. We find that the supersymmetric correlators are simple and natural generalizations of their non-supersymmetric counterparts. The notes are made to be self-contained and also include over $50$ exercises that illustrate the formalism.

[17] arXiv:2508.21757 (交叉列表自 math.RT) [中文pdf, pdf, html, 其他]

标题： Derksen-Weyman-Zelevinsky 无限维模的变异 I：基础 显示英文标题

标题： Derksen-Weyman-Zelevinsky mutations of infinite-dimensional modules I: Foundations

Daniel Labardini Fragoso

评论： 44页，1图

主题： 表示理论 (math.RT) ; 数学物理 (math-ph) ; 环与代数 (math.RA)

Derksen-Weyman-Zelevinsky 的箭图带势的有限维表示的变异理论被推广到无限维模的框架中。 显示英文摘要

Derksen-Weyman-Zelevinsky's mutation theory of finite-dimensional representations of quivers with potential is generalized to the framework of infinite-dimensional modules.

[18] arXiv:2508.21779 (交叉列表自 quant-ph) [中文pdf, pdf, html, 其他]

标题： 基于变形 su(1,1) 和海森堡代数的广义相干态的量子相位灵敏度 显示英文标题

标题： Quantum Phase Sensitivity with Generalized Coherent States Based on Deformed su(1,1) and Heisenberg Algebras

N.E. Abouelkhir, A. Slaoui, R. Ahl Laamara

主题： 量子物理 (quant-ph) ; 数学物理 (math-ph)

我们研究使用从广义Heisenberg和变形su(1,1)代数构造的广义相干态类的Mach Zehnder干涉仪的相位灵敏度。这些状态来源于具有四个参数变形谱的扰动谐振子，提供了增强的可调性和非经典特性。量子费舍尔信息及其相关的量子Cramér-Rao界限用于定义相位估计中的基本精度极限。我们分析了三种现实检测方法下的相位灵敏度：差分强度检测、单模强度检测和平衡外差检测。每种方法的性能与量子Cramér Rao界限进行比较以评估其最优性。我们的结果表明，在合适的参数范围内，这些广义相干态能够实现接近量子极限的相位灵敏度，为精密量子计量提供了一个灵活的框架。 显示英文摘要

We investigate the phase sensitivity of a Mach Zehnder interferometer using a special class of generalized coherent states constructed from generalized Heisenberg and deformed su(1,1) algebras. These states, derived from a perturbed harmonic oscillator with a four parameter deformed spectrum, provide enhanced tunability and nonclassical features. The quantum Fisher information and its associated quantum Cram\'er-Rao bound are used to define the fundamental precision limits in phase estimation. We analyze the phase sensitivity under three realistic detection methods: difference intensity detection, single mode intensity detection, and balanced homodyne detection. The performance of each method is compared with the quantum Cram\'er Rao bound to evaluate their optimality. Our results demonstrate that, for suitable parameter regimes, these generalized coherent states enable phase sensitivities approaching the quantum limit, offering a flexible framework for precision quantum metrology.

[19] arXiv:2508.21808 (交叉列表自 quant-ph) [中文pdf, pdf, html, 其他]

标题： 酉诱导信道和蒂塞朗森问题 显示英文标题

标题： Unitary induced channels and Tsirelson's problem

Michał Banacki, Paweł Horodecki

主题： 量子物理 (quant-ph) ; 数学物理 (math-ph)

受关于复合系统量子交换和量子张量模型的最新进展的启发，我们研究了一个(广义)酉诱导量子信道的概念。 利用布朗代数的性质，我们在张量和交换范式中提供了所讨论族的等价特征。 特别是，我们根据不需对无限维子系统进行测量的协议，以所考虑的范式为基础，提供了特塞尔森猜想(康尼斯嵌入问题)的等价表述。 作为结果，我们表明对于广义的酉诱导信道，量子交换模型和量子张量模型之间存在差异。 显示英文摘要

Motivated by a recent progress concerning quantum commuting and quantum tensor models of composed systems we investigate a notion of (generalized) unitary induced quantum channel. Using properties of Brown algebras we provide an equivalent characterization of discussed families in both tensor and commuting paradigms. In particular, we provide an equivalent formulation of Tsirelson's conjecture (Connes' embedding problem) in terms of considered paradigms based on protocols which do not require measurements performed on infinite-dimensional subsystems. As a result we show that there is a difference between quantum commuting and quantum tensor models for generalized unitary induced channels.

替换提交 (展示 18 之 18 条目 )

[20] arXiv:2206.10527 (替换) [中文pdf, pdf, html, 其他]

标题： 谱三元组和量子比特的康nes距离 显示英文标题

标题： Spectral triples and Connes distances of qubits

Bing-Sheng Lin, Zi-Hao Xu, Ji-Hong Wang, Han-Liang Chen

评论： 添加欧几里得距离和量子迹距离的狄拉克算子。欢迎提出评论

主题： 数学物理 (math-ph)

我们构建了一量子态和两量子态的谱三元组，并研究了康尼斯谱距离。 我们还构建了对应于正常量子迹距离的狄拉克算子。 基于康尼斯谱距离，我们定义了量子态的相干性度量，并计算了一量子态的相干性。 我们还研究了一些两量子态的简单情况，相应的谱距离满足勾股定理。 这些结果对于研究量子比特和其他量子态的物理关系和几何结构具有重要意义。 显示英文摘要

We construct spectral triples of one- and two-qubit states and study the Connes spectral distances. We also construct the Dirac operator corresponding to the normal quantum trace distances. Based on the Connes spectral distances, we define a coherence measure of quantum states, and calculate the coherence of one-qubit states. We also study some simple cases about two-qubit states, and the corresponding spectral distances satisfy the Pythagoras theorem. These results are significant for the study of physical relations and geometric structures of qubits and other quantum states.

[21] arXiv:2406.18874 (替换) [中文pdf, pdf, html, 其他]

标题： 时序几何的基本定理的最优版本 显示英文标题

标题： Optimal version of the fundamental theorem of chronogeometry

Michiya Mori, Peter Šemrl

评论： 70页

主题： 数学物理 (math-ph) ; 微分几何 (math.DG)

我们研究从$4$维闵可夫斯基时空$\mathcal{M}_4$到自身的保持类光性的映射，在没有任何额外的正则性假设（如连续性、满射性或单射性）的情况下。 我们证明这样的映射$\phi$满足以下三个条件中的一个。 (1) 映射$\phi$可以写成洛伦兹变换、正标量乘法和平移的复合。 (2) 存在一个事件$r\in \mathcal{M}_4$，使得$\phi(\mathcal{M}_4\setminus\{r\})$包含在一个光锥中。 (3) 存在一个类光直线$\ell$，使得$\phi(\mathcal{M}_4\setminus \ell)$包含在另一个类光直线中。 此处，包含在$\mathcal{M}_4$中某个光锥内的直线称为类光直线。 我们还给出了关于定义在$\mathcal{M}_4$的某个子集或$\mathcal{M}_4$的紧化空间上的映射的几个类似结果。 显示英文摘要

We study lightlikeness preserving mappings from the $4$-dimensional Minkowski spacetime $\mathcal{M}_4$ to itself under no additional regularity assumptions like continuity, surjectivity, or injectivity. We prove that such a mapping $\phi$ satisfies one of the following three conditions. (1) The mapping $\phi$ can be written as a composition of a Lorentz transformation, a multiplication by a positive scalar, and a translation. (2) There is an event $r\in \mathcal{M}_4$ such that $\phi(\mathcal{M}_4\setminus\{r\})$ is contained in one light cone. (3) There is a lightlike line $\ell$ such that $\phi(\mathcal{M}_4\setminus \ell)$ is contained in another lightlike line. Here, a line that is contained in some light cone in $\mathcal{M}_4$ is called a lightlike line. We also give several similar results on mappings defined on a certain subset of $\mathcal{M}_4$ or the compactification of $\mathcal{M}_4$.

[22] arXiv:2407.05030 (替换) [中文pdf, pdf, html, 其他]

标题： 关于多维相位恢复的非唯一性 显示英文标题

标题： On non-uniqueness of phase retrieval in multidimensions

Roman Novikov, Tianli Xu

评论： 我们对先前版本进行了重大修订

主题： 数学物理 (math-ph)

我们给出多维相位恢复问题非唯一性的一类大量例子。 我们的构造基于“斜张量化”，其中强烈地使用了一维结果，并将其推广以完全描述非唯一性。 我们的例子包括具有强不连通紧支集的函数的情况。 显示英文摘要

We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensional results are strongly used, and its generalizations towards complete description of non-uniqueness. Our examples include the case of functions with strongly disconnected compact support.

[23] arXiv:2409.10348 (替换) [中文pdf, pdf, html, 其他]

标题： 奇异(1+2)维福克-普朗克方程的广义对称性 显示英文标题

标题： Generalized symmetries of remarkable (1+2)-dimensional Fokker-Planck equation

Dmytro R. Popovych, Serhii D. Koval, Roman O. Popovych

评论： 30页，2张图表，发表版本，小幅度修改

主题： 数学物理 (math-ph) ; 偏微分方程分析 (math.AP) ; 环与代数 (math.RA)

使用一种原始方法，我们找到了一个显著的(1+2)维超抛物线Fokker-Planck方程的广义对称代数，该方程也称为Kolmogorov方程，并且由于其出色的对称性质而在所有具有三个自变量的超抛物线线性二阶偏微分方程类别中被突出显示。 结果表明，这个代数的基本子代数，由线性广义对称组成，是由Kolmogorov方程的基本李不变代数的幂零根相关的递归算子生成的，并且后者的莱维因子的Casimir算子意外地出现在考虑之中。 我们还建立了这个代数与第二个Weyl代数相关的李代数之间的同构，这为研究它们的性质提供了双重视角。 在发展了利用线性广义对称来寻找齐次线性微分方程组精确解的理论背景之后，我们将其有效地应用于Kolmogorov方程。 显示英文摘要

Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov equation and is singled out within the entire class of ultraparabolic linear second-order partial differential equations with three independent variables by its wonderful symmetry properties. It turns out that the essential subalgebra of this algebra, which consists of linear generalized symmetries, is generated by the recursion operators associated with the nilradical of the essential Lie invariance algebra of the Kolmogorov equation, and the Casimir operator of the Levi factor of the latter algebra unexpectedly arises in the consideration. We also establish an isomorphism between this algebra and the Lie algebra associated with the second Weyl algebra, which provides a dual perspective for studying their properties. After developing the theoretical background of finding exact solutions of homogeneous linear systems of differential equations using their linear generalized symmetries, we efficiently apply it to the Kolmogorov equation.

[24] arXiv:2412.03588 (替换) [中文pdf, pdf, 其他]

标题： 谱网络：连接高阶Teichmüller理论和BPS态 显示英文标题

标题： Spectral Networks: Bridging higher-rank Teichmüller theory and BPS states

Clarence Kineider, Georgios Kydonakis, Eugen Rogozinnikov, Valdo Tatitscheff, Alexander Thomas

评论： 514页，143图

主题： 数学物理 (math-ph) ; 高能物理 - 理论 (hep-th) ; 微分几何 (math.DG) ; 几何拓扑 (math.GT)

本书从一个统一的观点出发，全面介绍了谱网络，并将其与超对称规范理论的物理联系起来。 它提供了进入这一迅速发展的领域前沿所需的基础背景，同时并行处理几何和物理方面的问题。 在概述了代数和几何的基本主题后，详细介绍了高阶Teichmüller理论，包括Hitchin表示的Fock-Goncharov理论、极大表示以及最近提出的$\Theta$-正性概念。 随后介绍了谱网络，强调了它们在通过定义的阿贝尔化和非阿贝尔化映射来研究特征簇中的应用。 同时，探讨了具有八个超电荷的四维规范动力学的关键方面，包括电-磁对偶性、Seiberg-Witten理论以及类$\mathcal S$理论。 然后考察了谱网络在确定和分析类$\mathcal S$理论中BPS谱中的作用。 最后一章概述了谱网络在一系列当代研究领域的最新应用。 本卷旨在为希望进入该领域的数学或物理领域的研究人员和高年级学生提供参考。 显示英文摘要

This book offers a comprehensive introduction to spectral networks from a unified viewpoint that bridges geometry with the physics of supersymmetric gauge theories. It provides the foundational background needed to approach the frontiers of this rapidly evolving field, treating geometric and physical aspects in parallel. After surveying fundamental topics in algebra and geometry, a detailed introduction to higher-rank Teichm\"uller theory is developed, including Fock-Goncharov theory for Hitchin representations, maximal representations and the more recent notion of $\Theta$-positivity. Spectral networks are subsequently introduced, emphasizing their utility in the study of character varieties via the abelianization and non-abelianization maps they define. In parallel, key aspects of four-dimensional gauge dynamics with eight supercharges are explored, including electric-magnetic duality, Seiberg-Witten theory, and class $\mathcal S$ theories. The role of spectral networks as a framework for determining and analyzing BPS spectra in class $\mathcal S$ theories is then examined. The final chapter outlines recent applications of spectral networks across a range of contemporary research areas. This volume is intended for researchers and advanced students in either mathematics or physics who wish to enter the field.

[25] arXiv:2412.20483 (替换) [中文pdf, pdf, html, 其他]

标题： 曲率、面积和莫尔球的高斯-博内公式 显示英文标题

标题： Curvature, area and Gauss-Bonnet formula of the Moyal sphere

Han-Liang Chen, Bing-Sheng Lin

评论： 修复一些错误

期刊参考： J. 物理学 66, 083510 (2025)

主题： 数学物理 (math-ph) ; 高能物理 - 理论 (hep-th) ; 量子代数 (math.QA)

我们研究了Moyal球的一些几何性质。 使用普通空间中球的共形度量和矩阵基，我们计算了Moyal球的标量曲率、总曲率积分和面积。 我们发现当非对易参数趋近于0时，Moyal球的标量曲率和面积会恢复为普通球的值。 随着非对易参数的增加，Moyal球的面积将减少并最终趋近于0。 我们发现二维Moyal球的总曲率积分仍然满足通常的高斯-博内公式，并且不依赖于非对易参数。 我们还计算了具有常曲率的共形度量的近似表达式，并得到了相应的修正函数。 此外，我们研究了一种具有两个非对易参数的广义变形Moyal球，并得到了类似的结果。 显示英文摘要

We studied some geometric properties of the Moyal sphere. Using the conformal metric of the sphere in ordinary space and the matrix basis, we calculated the scalar curvature, total curvature integral and area of the Moyal sphere. We found that when the noncommutative parameter approaches to 0, the scalar curvature and area of the Moyal sphere return to those of the ordinary sphere. As the noncommutative parameter increases, the area of the Moyal sphere will decrease and eventually approach to 0. We found that the total curvature integral of the two-dimensional Moyal sphere still satisfies the usual Gauss-Bonnet formula and does not depend on the noncommutative parameter. We also calculated the approximate expression of the conformal metric with a constant curvature and obtained the corresponding correction function. In addition, we studied a type of generalized deformed Moyal sphere with two noncommutative parameters and obtained similar results.

[26] arXiv:2501.06592 (替换) [中文pdf, pdf, html, 其他]

标题： 量子伊辛模型的平均场行为和经典伊辛模型的新绳索展开 显示英文标题

标题： Mean-field behavior of the quantum Ising susceptibility and a new lace expansion for the classical Ising model

Yoshinori Kamijima, Akira Sakai

评论： 34页，22图

主题： 数学物理 (math-ph) ; 概率 (math.PR)

横场伊辛模型被广泛研究作为最简单的量子自旋系统之一。 已知该模型在临界逆温度$\beta_{\mathrm{c}}$处表现出相变，这由自旋-自旋耦合和横场$q \geq 0$确定。 Björnberg [Commun. Math. Phys., 232 (2013)] 研究了当以适当方式同时改变自旋-自旋耦合$J \geq 0$和$q$时，邻近自旋模型在接近临界点时磁化率的发散速率，温度保持固定。 在本文中，我们固定$J$和$q$并证明当$(\beta_{\mathrm{c}} - \beta)^{-1}$随着$\beta\uparrow\beta_{\mathrm{c}}$变化时，磁化率发散，对于$d>4$假设空间-时间两点函数的红外界限。 关键元素之一是 Björnberg & Grimmett [J. Stat. Phys., 136 (2009)] 和 Crawford & Ioffe [Commun. Math. Phys., 296 (2010)] 中的随机几何表示。 作为副产品，我们推导了经典伊辛模型（即，$q=0$）的新 lace 展开。 显示英文摘要

The transverse-field Ising model is widely studied as one of the simplest quantum spin systems. It is known that this model exhibits a phase transition at the critical inverse temperature $\beta_{\mathrm{c}}$, which is determined by the spin-spin couplings and the transverse field $q \geq 0$. Bj\"ornberg [Commun. Math. Phys., 232 (2013)] investigated the divergence rate of the susceptibility for the nearest-neighbor model as the critical point is approached by simultaneously changing the spin-spin coupling $J \geq 0$ and $q$ in a proper manner, with fixed temperature. In this paper, we fix $J$ and $q$ and show that the susceptibility diverges as $(\beta_{\mathrm{c}} - \beta)^{-1}$ as $\beta\uparrow\beta_{\mathrm{c}}$ for $d>4$ assuming an infrared bound on the space-time two-point function. One of the key elements is a stochastic-geometric representation in Bj\"ornberg & Grimmett [J. Stat. Phys., 136 (2009)] and Crawford & Ioffe [Commun. Math. Phys., 296 (2010)]. As a byproduct, we derive a new lace expansion for the classical Ising model (i.e., $q=0$).

[27] arXiv:2501.08041 (替换) [中文pdf, pdf, 其他]

标题： 范畴量子对称性和辫子张量2-范畴 显示英文标题

标题： Categorical quantum symmetries and ribbon tensor 2-categories

Hank Chen

评论： 53页（v1. 56页；删除了未使用的定义，增加了说明并简化了一些粘贴图）

主题： 数学物理 (math-ph) ; 范畴论 (math.CT) ; 量子代数 (math.QA)

在关于4d 2-Chern-Simons理论的组合量化的一篇相关工作中，作者构造了作用于格点上的离散表面-holonomy配置上的量子2-规范变换的Hopf范畴$\tilde{C}=\mathbb{U}_q\mathfrak{G}$。 我们在本文中证明了有限半单$\mathbb{C}$-线性$\tilde C$-模范畴的 2-$\mathsf{Hilb}$-丰富 2-表示 2-范畴$\operatorname{2Rep}(\tilde C)$是辫子的、平面-可逆的，并且是松紧的，因此$\operatorname{2Rep}(\tilde C)$提供了一个辫子张量 2-范畴的例子。 我们显式构造了辫子平衡函子，并展示了它们与紧致自伴结构的一致性条件。 这使得人们能够在具有对偶的2-范畴中精炼之前文献中研究过的各种\textit{框架}概念。 根据Baez-Langford的2扭结假说，可以构造出2扭结的框架不变量，这些不变量来自进入$\operatorname{2Rep}(\tilde C)$的丝带2-函子，类似于Reshetikhin-Turaev构造中装饰丝带图的定义。我们还将证明，在经典极限$q\rightarrow 1$下，2-范畴$\operatorname{2Rep}(\mathbb{U}_{q=1}\mathfrak{G})$在Douglas-Reutter的意义下变为严格前 pivotal。 显示英文摘要

In a companion work on the combinatorial quantization of 4d 2-Chern-Simons theory, the author has constructed the Hopf category of quantum 2-gauge transformations $\tilde{C}=\mathbb{U}_q\mathfrak{G}$ acting on the discrete surface-holonomy configurations on a lattice. We prove in this article that the 2-$\mathsf{Hilb}$-enriched 2-representation 2-category $\operatorname{2Rep}(\tilde C)$ of finite semisimple $\mathbb{C}$-linear $\tilde C$-module categories is braided, planar-pivotal, and lax rigid, hence $\operatorname{2Rep}(\tilde C)$ provides an example of a ribbon tensor 2-category. We explicitly construct the ribbon balancing functors, and exhibit their coherence conditions against the rigid dagger structures. This allows one to refine the various notions of \textit{framing} in a 2-category with duals that have been previously studied in the literature. Following the 2-tangle hypothesis of Baez-Langford, framed invariants of 2-tangles can then be constructed from ribbon 2-functors into $\operatorname{2Rep}(\tilde C)$, analogous to the definition of decorated ribbon graphs in the Reshetikhin-Turaev construction. We will also prove that, in the classical limit $q\rightarrow 1$, the 2-category $\operatorname{2Rep}(\mathbb{U}_{q=1}\mathfrak{G})$ becomes strict pivotal in the sense of Douglas-Reutter.

[28] arXiv:2403.04501 (替换) [中文pdf, pdf, html, 其他]

标题： Langevin方程和轴对称粒子旋转布朗运动的过阻尼极限的几何积分方案 显示英文标题

标题： Langevin equations and a geometric integration scheme for the overdamped limit of rotational Brownian motion of axisymmetric particles

Felix Höfling, Arthur V. Straube

评论： 已接受发表

主题： 统计力学 (cond-mat.stat-mech) ; 软凝聚态物理 (cond-mat.soft) ; 数学物理 (math-ph)

各向异性或自推进胶体粒子的平动运动与其取向及旋转布朗运动密切相关。 在过阻尼极限下，取向矢量的随机演化遵循单位球面上的扩散过程，并由一个与取向相关的（“乘法”）噪声所表征。 因此，相应的朗之万方程根据是否使用伊藤或斯特拉托诺维奇随机微积分而呈现出不同的形式。 我们阐明这两种形式是等价的，并通过基于无限小随机旋转的单位球面上布朗运动的几何构造，从上至下推导出它们。 我们的方法进一步提出了一种用于旋转布朗运动的几何积分方案，该方案能够精确保持取向矢量的归一化约束。 我们表明，基于高斯随机旋转的该方案的简单实现，在积分时间步长上具有弱收敛阶数为1的特性，并概述了该方案的一个高级变体，该变体对于任意大的时间步长都具有弱精确性。 由于离散化误差的有利前因子，仅高斯方案就允许比基于约束流形投影的常用旋转布朗动力学模拟算法大一个数量级的积分时间步长。 对于来自恒定外场的力矩，我们通过福克-普朗克方程证明，所构建的扩散过程满足细致平衡并收敛到正确的平衡分布。 该分析仅限于时间齐次的旋转布朗运动（即单一的旋转扩散常数），这对于轴对称粒子以及如自推进朱诺粒子这样的化学各向异性球体是相关的。 显示英文摘要

The translational motion of anisotropic or self-propelled colloidal particles is closely linked with the particle's orientation and its rotational Brownian motion. In the overdamped limit, the stochastic evolution of the orientation vector follows a diffusion process on the unit sphere and is characterized by an orientation-dependent (``multiplicative'') noise. As a consequence, the corresponding Langevin equation attains different forms depending on whether It\=o's or Stratonovich's stochastic calculus is used. We clarify that both forms are equivalent and derive them in a top-down appraoch from a geometric construction of Brownian motion on the unit sphere, based on infinitesimal random rotations. Our approach suggests further a geometric integration scheme for rotational Brownian motion, which preserves the normalization constraint of the orientation vector exactly. We show that a simple implementation of the scheme, based on Gaussian random rotations, converges weakly at order 1 of the integration time step, and we outline an advanced variant of the scheme that is weakly exact for an arbitrarily large time step. Due to a favorable prefactor of the discretization error, already the Gaussian scheme allows for integration time steps that are one order of magnitude larger compared to a commonly used algorithm for rotational Brownian dynamics simulations based on projection on the constraining manifold. For torques originating from constant external fields, we prove by virtue of the Fokker-Planck equation that the constructed diffusion process satisfies detailed balance and converges to the correct equilibrium distribution. The analysis is restricted to time-homogeneous rotational Brownian motion (i.e., a single rotational diffusion constant), which is relevant for axisymmetric particles and also chemically anisotropic spheres, such as self-propelled Janus particles.

[29] arXiv:2407.17334 (替换) [中文pdf, pdf, html, 其他]

标题： 稀薄传输的Navier-Stokes-Fourier方程扩展：玻尔兹曼方程的变分多尺度矩方法 显示英文标题

标题： Extensions to the Navier-Stokes-Fourier Equations for Rarefied Transport: Variational Multiscale Moment Methods for the Boltzmann Equation

F.A. Baidoo, I.M. Gamba, T.J.R. Hughes, M.R.A. Abdelmalik

主题： 流体动力学 (physics.flu-dyn) ; 数学物理 (math-ph)

我们推导了Navier-Stokes-Fourier方程在稀薄气体过渡区的四阶熵稳定扩展。我们通过一种新的重写方式，对从玻尔兹曼方程导出的守恒方程封闭进行处理，该方法涵盖了现有的方法，如查普曼-恩斯科格展开。我们将这种扩展的线性化版本应用于稳态热问题和泊肃叶通道，并将我们的解析解与线性化玻尔兹曼方程的渐近解和数值解进行比较。在两个模型问题中，我们的解在过渡区表现出显著的良好一致性。对于某些宏观变量，这种一致性甚至远远超出过渡区。 显示英文摘要

We derive a fourth order entropy stable extension of the Navier-Stokes-Fourier equations into the transition regime of rarefied gases. We do this through a novel reformulation of the closure of conservation equations derived from the Boltzmann equation that subsumes existing methods such as the Chapman-Enskog expansion. We apply the linearized version of this extension to the stationary heat problem and the Poiseuille channel and compare our analytical solutions to asymptotic and numerical solutions of the linearized Boltzmann equation. In both model problems, our solutions compare remarkably well in the transition regime. For some macroscopic variables, this agreement even extends far beyond the transition regime.

[30] arXiv:2409.12223 (替换) [中文pdf, pdf, html, 其他]

标题： 量子线性光学中的李代数不变量 显示英文标题

标题： Lie algebraic invariants in quantum linear optics

Pablo V. Parellada, Vicent Gimeno i Garcia, Julio José Moyano-Fernández, Juan Carlos Garcia-Escartin

评论： 18页，2张图表。欢迎提出意见！

主题： 量子物理 (quant-ph) ; 数学物理 (math-ph) ; 光学 (physics.optics)

没有后选择的量子线性光学不足以从给定的输入态生成任何量子态。 这限制了其应用，因为一些应用需要难以制备的纠缠资源。 因此，我们需要对线性光学态制备有更深入的理解。 在本工作中，我们提供了一个方法，用于推导任意态在任何可能的无源线性干涉仪演化中的守恒量。 这样的不变量的一个例子是密度算符在无源线性光学哈密顿量李代数上的投影。 这些不变量给出了精确态制备的必要条件：如果输入态和输出态具有不同的不变量，则不可能设计一个无源线性干涉仪将其中一个演化为另一个。 此外，我们基于它们的不变量之间的距离，给出了输出态与目标态之间距离的下限。 这为近似或后选择态制备提供了必要条件。 因此，这些不变量使我们在尝试从易于制备的态（如福克态）制备有用的纠缠态（如NOON态）时，能够缩小搜索范围。 我们得出结论，未来的精确和近似态制备方法需要考虑由我们的不变量给出的必要条件，以排除不可能的线性光学演化。 显示英文摘要

Quantum linear optics without post-selection is not powerful enough to produce any quantum state from a given input state. This limits its utility since some applications require entangled resources that are difficult to prepare. Thus, we need a deeper understanding of linear optical state preparation. In this work, we give a recipe to derive conserved quantities in the evolution of arbitrary states along any possible passive linear interferometer. One example of such an invariant is the projection of a density operator onto the Lie algebra of passive linear optical Hamiltonians. These invariants give necessary conditions for exact state preparation: if the input and output states have different invariants, it is impossible to design a passive linear interferometer that evolves one into the other. Moreover, we provide a lower bound to the distance between an output and target state based on the distance between their invariants. This gives a necessary condition for approximate or heralded state preparations. Therefore, the invariants allow us to narrow the search when trying to prepare useful entangled states, like NOON states, from easy-to-prepare states, like Fock states. We conclude that future exact and approximate state preparation methods will need to consider the necessary conditions given by our invariants to weed out impossible linear optical evolutions.

[31] arXiv:2410.10375 (替换) [中文pdf, pdf, 其他]

标题： 振荡类时奇点：Bianchi类型$\mathrm{VI}_{-1/9}$真空模型 显示英文标题

标题： Oscillatory spacelike singularities: The Bianchi type $\mathrm{VI}_{-1/9}$ vacuum models

Phillipo Lappicy, Claes Uggla

评论： 65页，24图

主题： 广义相对论与量子宇宙学 (gr-qc) ; 数学物理 (math-ph) ; 动力系统 (math.DS)

比安基类型$\mathrm{VI}_{-1/9}$、$\mathrm{VIII}$和$\mathrm{IX}$的真空模型都有4维的哈勃归一化状态空间，并预期具有一般的初始振荡奇点，但导致振荡的不变边界集对于类型$\mathrm{VI}_{-1/9}$来说比类型$\mathrm{VIII}$和$\mathrm{IX}$的要复杂得多。 首次，我们明确求解了这些类型$\mathrm{VI}_{-1/9}$边界集上的方程，并引入了一种新的图表示方法来描述相关的异宿链网络（即描述振荡的解序列）。 特别是，我们给出了纠缠循环异宿链网络的例子，并表明只有其中一些循环异宿链在渐近意义上是相关的。 显示英文摘要

The Bianchi type $\mathrm{VI}_{-1/9}$, $\mathrm{VIII}$ and $\mathrm{IX}$ vacuum models all have 4-dimensional Hubble-normalized state spaces and are expected to have a generic initial oscillatory singularity, but the invariant boundary sets responsible for the oscillations are much more complicated for type $\mathrm{VI}_{-1/9}$ than those of type $\mathrm{VIII}$ and $\mathrm{IX}$. For the first time, we explicitly solve the equations on these type $\mathrm{VI}_{-1/9}$ boundary sets and also introduce a new graph representation of the associated network of heteroclinic chains (i.e. sequences of solutions describing the oscillations). In particular, we give examples of networks of entangled cyclic heteroclinic chains and show that only some of these cyclic heteroclinic chains are asymptotically relevant.

[32] arXiv:2502.15627 (替换) [中文pdf, pdf, html, 其他]

标题： 超对称规范理论中的施瓦茨希尔德时空中的大矢量场扰动 显示英文标题

标题： Massive vector field perturbations in the Schwarzschild spacetime from supersymmetric gauge theory

Xian-Hui Ge, Masataka Matsumoto, Kilar Zhang

评论： 19页，3张表格，2幅图；v2：小幅度修改，发表版本

主题： 高能物理 - 理论 (hep-th) ; 高能天体物理现象 (astro-ph.HE) ; 广义相对论与量子宇宙学 (gr-qc) ; 高能物理 - 现象学 (hep-ph) ; 数学物理 (math-ph)

我们通过Seiberg-Witten/准正则模态(SW/QNM)对偶，将Schwarzschild时空中质量矢量(Proca)场的动力学与超对称规范理论统一起来。 通过将Proca扰动——特别是由合流Heun方程支配的单极子和奇宇称模式——映射到量子Seiberg-Witten曲线，我们建立了规范-引力对应关系。 利用瞬子计数，我们精确地解析计算了QNM和准束缚态频率，非微扰地解决了光谱特性。 我们的结果与数值基准一致，同时将SW框架扩展到了标量场之外。 显示英文摘要

We unify the dynamics of massive vector (Proca) fields in Schwarzschild spacetime with supersymmetric gauge theories through the Seiberg-Witten/quasinormal mode (SW/QNM) duality. By mapping Proca perturbations-specifically monopole and odd-parity modes governed by confluent Heun equations-to the quantum Seiberg-Witten curve, we establish a gauge-gravity correspondence. Leveraging instanton counting, we analytically compute QNM and quasi-bound state frequencies to high precision, resolving spectral properties non-perturbatively. Our results align with numerical benchmarks while extending the SW framework beyond scalar fields.

[33] arXiv:2502.20444 (替换) [中文pdf, pdf, html, 其他]

标题： 等变拓扑弦中的常值映射和通量的几何建模 显示英文标题

标题： Constant maps in equivariant topological strings and geometric modeling of fluxes

Luca Cassia, Kiril Hristov

评论： 59页+附录和参考文献；v2小修正和新增参考文献；v3改进了讨论并新增附录；

主题： 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph)

我们研究了在 торic 流形上的拓扑弦的等变推广，特别关注于在划分函数的亏格展开中定义常值映射的贡献。 这种方法对非紧致 Calabi-Yau 空间进行了正则化，使得展开中的每一阶都能得到有限的结果，如一系列明确的例子所示。 我们的研究强调了通量紧化几何建模，并澄清了有效超重力框架与等变拓扑弦形式之间的联系，这是基于 Martelli 和 Zaffaroni 的最新发展。 我们得出结论，拓扑弦理论与超引力/场论之间的联系涉及几何模数和通量之间的转换，这揭示了弦理论中系综平均的作用。 我们提出了一种与相应 M2-膜划分函数精确的非微扰全息匹配，在附带论文中，我们在规范群秩$N$的所有阶次下对其进行了微扰测试。 我们提议的一个特殊情形在通量为零的情况下，在等变拓扑弦框架内重新表述了 Ooguri--Strominger--Vafa 猜想。 显示英文摘要

We study the equivariant generalization of topological strings on toric manifolds, focusing in particular on defining the contributions of constant maps in the genus expansion of the partition function. This approach regularizes the integration over non-compact Calabi-Yau spaces, producing finite results at each order in the expansion, as illustrated by a broad set of explicit examples. Our investigation highlights the geometric modeling of flux compactifications and clarifies the link between the effective supergravity framework and the equivariant topological string formalism, building on recent developments by Martelli and Zaffaroni. We conclude that the connection between topological string theory and supergravity/field theory involves switching between geometric moduli and fluxes, shedding light on the role of ensemble averages in string theory. We propose an exact non-perturbative holographic match with the corresponding M2-brane partition functions, which we test perturbatively at all orders in the gauge group rank $N$ in a companion paper. A special case of our proposal for vanishing flux reformulates the Ooguri--Strominger--Vafa conjecture within the equivariant topological string framework.

[34] arXiv:2504.06248 (替换) [中文pdf, pdf, html, 其他]

标题： 库拉莫托遇见库普曼：运动常数、对称性和网络基序 显示英文标题

标题： Kuramoto meets Koopman: Constants of motion, symmetries, and network motifs

Vincent Thibeault, Benjamin Claveau, Antoine Allard, Patrick Desrosiers

主题： 适应性与自组织系统 (nlin.AO) ; 数学物理 (math-ph) ; 精确可解与可积系统 (nlin.SI)

利用Koopman生成元的谱性质，我们推导了在任意加权、有向、带符号图上具有异质相位滞后性的Kuramoto模型中存在不同守恒量的必要且充分条件。我们还识别出生成新守恒量的李对称性。这些结果揭示了一类广泛的网络模块，它们支持守恒量，并说明了一个领导者如何驱动一群顺应-反叛振荡器达到具有更高平均同步性甚至完美同步性的周期状态。 显示英文摘要

Using spectral properties of the Koopman generator, we derive necessary and sufficient conditions for the existence of distinct constants of motion in the Kuramoto model with heterogeneous phase lags on any weighted, directed, signed graph. We also identify Lie symmetries that generate new constants of motion. These results reveal a broad class of network motifs that support conserved quantities and how a leader drives a group of conformist-contrarian oscillators to reach periodic states with higher average synchrony or even perfect synchrony.

[35] arXiv:2505.17044 (替换) [中文pdf, pdf, html, 其他]

标题： 球面上的热准地转模型：推导与结构保持模拟 显示英文标题

标题： Thermal quasi-geostrophic model on the sphere: derivation and structure-preserving simulation

Michael Roop, Sagy Ephrati

评论： 17页，9张图，增加了说明和一张图，更正了拼写错误

主题： 数值分析 (math.NA) ; 数学物理 (math-ph) ; 流体动力学 (physics.flu-dyn)

我们通过热旋转浅水方程的渐近展开推导了球面上的全局热准地转模型。该模型不依赖科里奥利力的渐近展开，并通过包括一个额外的输运浮力场来扩展球面上的准地转模型，该场作为位势涡度的源项。我们给出了其以半直积李-泊松括号形式的哈密顿描述。哈密顿公式揭示了存在无限多个守恒定律，即卡西米尔，这些由两个任意光滑函数参数化。基于泽特林为流体力学提出的自洽矩阵近似，提供了一种保持结构的离散化方法。采用保持卡西米尔的时间积分器，以数值上完全保留所得的有限维李-泊松结构。模拟结果揭示了涡度和浮力前沿的形成，以及由浮力-地形相互作用引起的浮力动力学中的大尺度结构。 显示英文摘要

We derive the global model of thermal quasi-geostrophy on the sphere via asymptotic expansion of the thermal rotating shallow water equations. The model does not rely on the asymptotic expansion of the Coriolis force and extends the quasi-geostrophic model on the sphere by including an additional transported buoyancy field acting as a source term for the potential vorticity. We give its Hamiltonian description in terms of semidirect product Lie--Poisson brackets. The Hamiltonian formulation reveals the existence of an infinite number of conservation laws, Casimirs, parameterized by two arbitrary smooth functions. A structure-preserving discretization is provided based on Zeitlin's self-consistent matrix approximation for hydrodynamics. A Casimir-preserving time integrator is employed to numerically fully preserve the resulting finite-dimensional Lie--Poisson structure. Simulations reveal the formation of vorticity and buoyancy fronts, and large-scale structures in the buoyancy dynamics induced by the buoyancy-bathymetry interaction.

[36] arXiv:2505.20260 (替换) [中文pdf, pdf, 其他]

标题： 关于A多项式的几何基第二部分：$\mathfrak{su}_3$和 Kuberberg括号 显示英文标题

标题： On geometric bases for A-polynomials II: $\mathfrak{su}_3$ and Kuberberg bracket

Dmitry Galakhov, Alexei Morozov

评论： 26页，8图，v2：小的更正，添加了参考文献

期刊参考： 欧洲物理杂志C 85, 915 (2025)

主题： 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph) ; 几何拓扑 (math.GT) ; 量子代数 (math.QA)

我们继续研究量子A多项式——关于结多项式与其着色（表示依赖性）的方程——作为通过在原始结上悬挂额外的“简单”成分而得到的不同链接之间的关系。 根据这种“装饰”的选择，结多项式要么乘以一个数，要么通过编织过程分解为“周围”表示的和。 发生的情况是，这些两种装饰，当足够复杂时，会变得相关——这提供了一个方程。 值得注意的是，这个方程可以独立于表示。 然而，链接的等价性不是一个拓扑性质——它来自于$R$-矩阵的性质，并且强烈依赖于规范群的选择和特定的链接。 故事中相对被深入研究的部分涉及$\mathfrak{su}_2$，其中$R$-矩阵可以选择一种特别方便的Kauffman形式，这使得方程的推导相当几何化。 为了使这些几何方法更简单一些，我们建议使用辫群的拱门形式/表示来普遍简化链接的装饰。 在这里，我们尝试将这种技术扩展到下一个情况$\mathfrak{su}_3$，在这里Kauffman规则被更复杂的Kuberberg规则所取代，仍然比需要用于更高秩的MOY图的一般分析更几何化。 即使在这种情况，我们也遇到了可能的“装饰”分类问题以及在表示计数中出现的两行Young图。 显示英文摘要

We continue the study of quantum A-polynomials -- equations for knot polynomials with respect to their coloring (representation-dependence) -- as the relations between different links, obtained by hanging additional ``simple'' components on the original knot. Depending on the choice of this ``decoration'', the knot polynomial is either multiplied by a number or decomposes into a sum over ``surrounding'' representations by a cabling procedure. What happens is that these two of decorations, when complicated enough, become dependent -- and this provides an equation. Remarkably it can be made independent of the representation. However, the equivalence of links is not a topological property -- it follows from the properties of $R$-matrices, and strongly depends on the choice the gauge group and particular links. The relatively well studied part of the story concerns $\mathfrak{su}_2$, where $R$-matrices can be chosen in an especially convenient Kauffman form, what makes the derivation of equations rather geometrical. To make these geometric methods somewhat simpler we suggest to use an arcade formalism/representation of the braid group to simplify decorating links universally. Here we attempt to extend this technique to the next case, $\mathfrak{su}_3$, where the Kauffman rule is substituted by a more involved Kuberberg rule, still remains more geometric than generic analysis of MOY-diagrams, needed for higher ranks. Already in this case we encounter a classification problem for possible ``decorations'' and emergence of two-lined Young diagrams in enumeration of representations.

[37] arXiv:2506.06700 (替换) [中文pdf, pdf, html, 其他]

标题： 量子可访问信息和经典熵不等式 显示英文标题

标题： Quantum accessible information and classical entropy inequalities

A. S. Holevo, A. V. Utkin

评论： 41页，无图表。论点得到改进，拼写错误已更正

主题： 量子物理 (quant-ph) ; 信息论 (cs.IT) ; 数学物理 (math-ph)

计算量子态集合的可访问信息是量子信息理论中的一个基本问题。 我们表明，最近在[7]中获得的最优性准则，当应用于特定的态集合时，会导致香农熵的非平凡紧下界，这些下界是著名的对数 Sobolev 不等式的离散类比。 从这个角度来看，文献[2]中提出的并数值验证的关于等角等概率态集合（量子金字塔）全局信息最优测量的假设被重新考虑，并提出了相应的紧熵不等式。 通过最优性准则，这也暗示了对文献[2]中提出的关于量子金字塔全局信息最优可观测量的猜想的证明。 显示英文摘要

Computing accessible information for an ensemble of quantum states is a basic problem in quantum information theory. We show that the optimality criterion recently obtained in [7], when applied to specific ensembles of states, leads to nontrivial tight lower bounds for the Shannon entropy that are discrete relatives of the famous log-Sobolev inequality. In this light, the hypothesis of globally information-optimal measurement for an ensemble of equiangular equiprobable states (quantum pyramids) put forward and numerically substantiated in [2] is reconsidered and the corresponding tight entropy inequalities are proposed. Via the optimality criterion, this suggests also a proof of the conjecture concerning globally information-optimal observables for quantum pyramids put forward in [2].