非线性科学
查看 最近的 文章
显示 2026年05月14日， 星期四 新的列表
- [1] arXiv:2605.12605 [中文pdf, pdf, html, 其他]
-
标题： 局部解在格子动力系统中的稳定性标题： Stability of localized solutions to lattice dynamical systems评论： 31页，9图主题： 模式形成与孤子 (nlin.PS)
局部模式是出现在格子动力系统中的空间限制结构，在物理学、生物学和材料科学中起着重要作用。 虽然它们的存在性和分岔结构已经得到了很好的理解，但这些解的稳定性在离散和高维设置中仍然 largely 未被探索。 在本工作中，我们开发了一个通用的理论框架，用于分析一维和多维矩形格子中局部稳态的谱稳定性。 我们的方法利用了前缘和后缘解的性质，结合离散 Evans 函数公式，以表征局部解的谱。 我们证明了，对于分离的局部区域，Evans 函数渐近地分解为来自基础前缘和后缘的贡献，从而允许对不稳定的特征值进行显式计数。 该框架适用于具有单个或多个平台的解，包括振荡和多脉冲配置。 我们在一个实值的三次五次 Ginzburg-Landau 格子、一个典型的 Nagumo 类型系统上展示了结果，并提供了分岔结构和特征值谱的数值演示。
Localized patterns are spatially confined structures that arise in lattice dynamical systems and play an important role in physics, biology, and materials science. While their existence and bifurcation structure are well-understood, the stability of these solutions remains largely unexplored, particularly in discrete and high-dimensional settings. In this work, we develop a general theoretical framework to analyze the spectral stability of localized steady states in one-dimensional and multi-dimensional rectangular lattices. Our approach leverages the properties of front and back solutions, combined with a discrete Evans function formulation, to characterize the spectrum of localized solutions. We prove that, for well-separated regions of localization, the Evans function asymptotically factorizes into contributions from the underlying fronts and backs, allowing explicit counting of unstable eigenvalues. This framework applies to solutions with single or multiple plateaus, including oscillatory and multi-pulse configurations. We illustrate the results on a real-valued cubic-quintic Ginzburg-Landau lattice, a prototypical Nagumo-type system, and provide numerical demonstrations of bifurcation structures and eigenvalue spectra.
- [2] arXiv:2605.12633 [中文pdf, pdf, html, 其他]
-
标题： 虚假真空孤立子的碰撞动力学标题： Collision Dynamics of False-Vacuum Oscillons主题： 高能物理 - 理论 (hep-th) ; 模式形成与孤子 (nlin.PS)
我们研究了在具有亚稳态假真空的两类$(1+1)$维标量场理论中局域振子的碰撞动力学，一类是具有正四次自相互作用项的正常类，另一类是具有负四次项的倒置类。 我们使用 Fodor{\emph{等.}}展开在假真空附近构造了小振幅振子解，并表明振子之间的力在大距离处呈指数衰减，其强度由它们的相对相位调制。 两个振子碰撞的数值模拟显示了反射、穿过以及激发振子的形成。 出现共振窗口，类似于在孤子-反孤子碰撞中发现的情况。 在正常理论中，如果振子具有足够的能量，场可以越过 sphaleron 障碍并演化成一个孤子-反孤子对，从而引发向真真空的相变。 我们还模拟了从略微扰动的 sphaleron 演化而来的振子碰撞。
We study the collision dynamics of localized oscillons in two classes of $(1+1)$-dimensional scalar field theories with metastable false vacua, a normal class with a positive quartic self-interaction term and an inverted class with a negative quartic term. We construct small-amplitude oscillon solutions around the false vacuum using the Fodor {\emph{et al.}} expansion, and show that the force between oscillons decays exponentially at large separation, with a strength modulated by their relative phase. Numerical simulations of two-oscillon collisions exhibit reflection, crossing, and formation of excited oscillons. Resonance windows occur, similar to those found in kink-antikink collisions. In the normal theory, if the oscillons have sufficient energy, the field can pass over a sphaleron barrier and evolve into a kink-antikink pair, initiating a phase transition to the true vacuum. We also simulate the collision of oscillons evolved from a slightly perturbed sphaleron.
- [3] arXiv:2602.17444 [中文pdf, pdf, html, 其他]
-
标题： 在使用叶瓣动力学序列的地月空间中低能量轨道设计标题： Design of low-energy transfers in cislunar space using sequences of lobe dynamics评论： 53页，51幅图。提交至《航天器》期刊主题： 混沌动力学 (nlin.CD) ; 天体物理学的仪器与方法 (astro-ph.IM) ; 动力系统 (math.DS) ; 优化与控制 (math.OC) ; 经典物理 (physics.class-ph)
在圆型限制三体问题（CR3BP）中，动态结构对于设计低能量转移是基本的，因为它们有助于分析相空间传输并设计理想的轨迹。 这些动态结构之一，瓣状动力学，可以被利用来实现天体周围的局部混沌传输。 本研究提出并完全验证了一种系统方法，通过结合多个瓣状动力学序列来设计低能量转移，建立在作者之前初步框架的基础上。 开发了一个基于图的框架，以探索出发轨道和到达轨道之间的可能传输路径，从而降低燃料高效传输设计的组合优化问题的复杂性。 使用该图，通过连接瓣状内的混沌轨道来构建低能量传输轨迹。 然后将地球-月球CR3BP中的最优轨迹通过多次射击转换为双圆限制四体问题中的最优传输。 该传输与现有最优解进行比较，以证明所提出方法的有效性。
Dynamical structures in the circular restricted three-body problem (CR3BP) are fundamental for designing low-energy transfers, as they aid in analyzing phase space transport and designing desirable trajectories. One of these dynamical structures, lobe dynamics, can be exploited to achieve local chaotic transport around celestial bodies. This study proposes and fully validates a systematic method for designing low-energy transfers by combining multiple sequences of lobe dynamics, building upon the authors' prior preliminary framework. A graph-based framework is developed to explore possible transfer paths between departure and arrival orbits, reducing the complexity of the combinatorial optimization problem for fuel-efficient transfer design. Using this graph, low-energy transfer trajectories are constructed by connecting chaotic orbits within lobes. The resulting optimal trajectory in the Earth--Moon CR3BP is then converted into an optimal transfer in the bicircular restricted four-body problem via multiple shooting. This transfer is compared with existing optimal solutions to demonstrate the effectiveness of the proposed method.
- [4] arXiv:2511.10115 [中文pdf, pdf, html, 其他]
-
标题： 二维吸引相互作用玻色子的广义Gross-Pitaevskii方程标题： Generalized Gross-Pitaevskii Equation for 2D Bosons with Attractive Interactions主题： 量子气体 (cond-mat.quant-gas) ; 模式形成与孤子 (nlin.PS) ; 核理论 (nucl-th) ; 原子与分子簇 (physics.atm-clus)
我们引入了一个广义的Gross-Pitaevskii方程，该方程为研究二维（2D）吸引玻色系统提供了一个非线性框架。其显著特点是耦合常数的对数密度依赖性，这打破了标准平均场方程中固有的尺度不变性。该框架允许直接计算由量子异常产生的系统特性。作为首次展示，我们研究了自由空间中的普遍束缚态，通常称为量子液滴。然后，我们分析了束缚系统中的呼吸模式和淬火动力学，为系统地探索二维吸引玻色系统中的非平衡现象铺平了道路。最后，我们预测了普遍激发态的存在，包括涡旋配置，这些可能比基态更容易进行实验研究。我们的结果为研究有限系统的静态和动态特性提供了坚实的理论基础，并为未来实验的设计提供了指导。
We introduce a generalized Gross-Pitaevskii equation that provides a nonlinear framework for studying two-dimensional (2D) attractive Bose systems. Its defining feature is the logarithmic density dependence of the coupling constant, which breaks the scale invariance inherent in the standard mean-field equations. This framework allows straightforward calculations of the system properties arising from the quantum anomaly. As a first illustration, we study universal bound states in free space, commonly referred to as quantum droplets. Then, we analyze breathing modes and quench dynamics in trapped systems, paving the way for a systematic exploration of non-equilibrium phenomena in 2D attractive Bose systems. Finally, we predict the existence of universal excited states, including vortex configurations, which may be more accessible to experimental investigation than the ground state. Our results provide a robust theoretical foundation for studying both static and dynamical properties of finite systems, and offer guidance for the design of future experiments.
新提交 (展示 4 之 4 条目 )
- [5] arXiv:2509.18279 (交叉列表自 nlin.AO) [中文pdf, pdf, 其他]
-
标题： 最优同步网络的涌现拓扑结构标题： Emergent Topology of Optimal Networks for Synchrony评论： 16页，5图主题： 适应性与自组织系统 (nlin.AO) ; 统计力学 (cond-mat.stat-mech)
设计高性能网络需要在尊重物理、几何或预算约束的同时优化功能。 然而，用于设计此类系统的数学和计算工具仍然有限，特别是对于来自异构动力学单元的集体动态。 在这里，我们开发了一个基于梯度的优化框架，在受限耦合预算下确定同步最优加权网络。 这些网络表现出反直觉的特性：它们是稀疏的、二分的、细长的，并且极度单向（即，任何节点的邻居彼此相似，而与该节点本身不同）。 这些结构模式在从电力网摆动方程到混沌Rössler系统的动力学模型中都存在，表明其在耦合振荡器技术中的广泛应用前景。 为了获得洞察，我们为耦合的Kuramoto振荡器开发了一种“构造性”理论：一个非线性微分方程确定哪些节点对被耦合，而一个变分原理规定了每个节点分配的预算。 在最优网络上展开的动力学证明缺乏同步阈值；相反，当预算超过可计算的关键值时，系统会全局相位锁定，在转换过程中表现出临界标度。 我们的研究结果共同为依赖同步的技术提供了设计原则，潜在应用范围从微电网到激光阵列和量子振荡器。
Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for collective dynamics arising from heterogeneous dynamical units. Here, we develop a gradient-based optimization framework to identify synchrony-optimal weighted networks under a constrained coupling budget. The resulting networks exhibit counterintuitive properties: they are sparse, bipartite, elongated, and extremely monophilic (i.e., the neighbors of any node are similar to one another while differing from the node itself). These structural patterns persist across dynamical models ranging from the power-grid swing equations to chaotic Rössler systems, suggesting broad applicability to coupled oscillator technologies. To gain insight, we develop a "constructive" theory for coupled Kuramoto oscillators: a nonlinear differential equation identifies which pairs of nodes are coupled, while a variational principle prescribes the budget allocated to each node. Dynamics unfolding over optimal networks provably lack a synchronization threshold; instead, as the budget exceeds a calculable critical value, the system globally phase-locks, exhibiting critical scaling at the transition. Together, our findings offer design principles for synchrony-dependent technologies with potential applications ranging from microgrids to laser arrays and quantum oscillators.
- [6] arXiv:2605.13463 (交叉列表自 nlin.SI) [中文pdf, pdf, html, 其他]
-
标题： 关于达布-哈尔phen系统：雅可比与李标题： On the Darboux-Halphen system: Jacobi vs Lie评论： 12页，LaTeX使用AMS字体主题： 精确可解与可积系统 (nlin.SI) ; 数学物理 (math-ph) ; 动力系统 (math.DS)
讨论了Darboux-Halphen系统的两种构造方法。 在Jacobi构造中，我们从多值函数出发，这些函数被固定为首次积分。 在Lie构造中，我们使用简单代数的单值表示，在Lie的术语中这是不可积的。
Two constructions of the Darboux-Halphen system are discussed. In the Jacobi construction we start with multi-valued functions which are fixed as the first integrals. In the Lie construction we use single-valued representation of the simple algebra which is non-integrable in Lie's terminology.
- [7] arXiv:2605.13354 (交叉列表自 nlin.CD) [中文pdf, pdf, html, 其他]
-
标题： 基于单个约瑟夫森结的储层计算标题： Reservoir Computing with a single Josephson junction主题： 混沌动力学 (nlin.CD)
物理储备计算利用物理系统的非线性动力学来执行信息处理任务。 约瑟夫森结（JJs）作为具有丰富动态行为的非线性超导器件，是储备计算中有前景但相对未被探索的候选者。 在本工作中，我们首次证明，单个约瑟夫森结可以在不使用显式延迟环的情况下用作储备计算基底。 通过数值模拟，我们分析了不同动力学状态下储备性能，并表明当JJ在稳定但响应性的状态下运行时，可以实现最佳性能。 尽管没有延迟反馈，JJ通过其内在动力学表现出足够的记忆能力，从而在混沌时间序列预测任务中取得良好性能。 此外，我们探索了一种基于连续调制的替代输入掩码方法，突出了其与实际实现的兼容性。 这些结果确立了约瑟夫森结作为一种可行且高效的储备计算平台，并为超快速、低耗散的硬件实现开辟了道路。
Physical reservoir computing exploits the nonlinear dynamics of a physical system to perform information processing tasks. Josephson junctions (JJs), as nonlinear superconducting devices with rich dynamical behavior, represent promising yet relatively unexplored candidates for reservoir computing. In this work, we demonstrate for the first time that a single Josephson junction can be employed as a reservoir computing substrate without the use of an explicit delay loop. Using numerical simulations, we analyze the reservoir performance in different dynamical regimes and show that optimal performance is achieved when the JJ operates in a stable yet responsive regime. Despite the absence of delayed feedback, the JJ exhibits sufficient memory through its intrinsic dynamics to achieve good performance on a chaotic time series prediction task. In addition, we explore an alternative input masking approach based on continuous modulation, highlighting its compatibility with practical implementations. These results establish Josephson junctions as a viable and efficient platform for reservoir computing and open the way to ultrafast, low-dissipation hardware realizations.
- [8] arXiv:2605.13654 (交叉列表自 physics.flu-dyn) [中文pdf, pdf, html, 其他]
-
标题： 由三维湍流引起的自由面变形标题： Free-surface deformations induced by three-dimensional turbulence主题： 流体动力学 (physics.flu-dyn) ; 混沌动力学 (nlin.CD) ; 大气与海洋物理 (physics.ao-ph) ; 经典物理 (physics.class-ph)
我们报告了由三维均匀各向同性湍流产生的自由表面变形的实验表征。 使用喷射驱动湍流水箱中的傅里叶变换轮廓测量法，我们在不同湍流强度范围内对表面高度场进行了时空测量。 表面变形的标准差与次表面速度波动成线性关系。 表面变形的谱图突显了两种机制的共存：瞬态相干结构（例如上升流）对低频、大尺度谱成分的贡献，以及对次表面湍流压力波动的被动响应，后者负责幂律谱标度。 表面变形的波数和频率谱表现出相似的幂律指数（-2.5），表明湍流结构在自由表面上的输运。 我们基于自由表面到湍流压力波动的传递函数开发了一个线性响应模型，并结合了波-湍流阻尼。 该模型成功预测了湍流表面的主要特征：时空谱形状、相似的谱幂律指数（-7/3），以及被动响应对波生成的主导作用。 这些发现为湍流速度仍低于表面破裂阈值的自由表面湍流提供了新的见解。
We report the experimental characterization of free-surface deformations generated by three-dimensional homogeneous and isotropic turbulence. Using Fourier transform profilometry in a jet-forced turbulent tank, we perform spatiotemporal measurements of the surface elevation field over a wide range of turbulence intensities. The standard deviation of surface deformations scales linearly with subsurface velocity fluctuations. The spectra of surface deformations highlight the coexistence of two mechanisms: transient coherent structures (e.g., upwelling) contributing to the low-frequency, large-scale spectral components, and a passive response to subsurface turbulent pressure fluctuations responsible for the power-law spectral scaling. The wavenumber and frequency spectra of surface deformations exhibit similar power-law exponents (-2.5), suggesting the advection of turbulent structures at the free surface. We develop a linear response model based on the transfer function from the free surface to turbulent pressure fluctuations, incorporating wave-turbulent damping. The model successfully predicts the main features of the turbulent surface: spatiotemporal spectrum shape, similar spectrum power-law exponents (-7/3), and dominance of passive response over wave generation. These findings provide new insights into free-surface turbulence in regimes where turbulent velocities remain below the surface-breaking threshold.
交叉提交 (展示 4 之 4 条目 )
- [9] arXiv:2605.12533 (替换) [中文pdf, pdf, html, 其他]
-
标题： 克劳普振荡器中混沌行为的调查标题： Investigation of Chaotic Behavior in Clapp Oscillator期刊参考： IcETRAN-2018，帕利奇，塞尔维亚，2018主题： 系统与控制 (eess.SY) ; 混沌动力学 (nlin.CD)
在本文中，我们研究了称为Clapp振荡器的振荡器类别的混沌行为。 Clapp振荡器是一种包含一个晶体管和几个无源元件（电感器和电容器）的简单振荡器。 该振荡器因其设计简单和良好的性能而被选用。 具有混沌行为的振荡器可以用于构建混沌雷达。 为此，在本文中研究了构建混沌Clapp振荡器的方法，该方法可以进一步通过微带技术进行实验验证。
In this paper we investigate the chaotic behavior of the class of oscillators denoted as Clapp oscillators. Clapp oscillator is a simple oscillator containing one transistor and a few reactive elements - inductors and capacitors. This oscilllator is chosen for its design simplicity and a good performance. Oscillator with chaotic behavior can be used to construct chaotic radar. For that matter, in this paper is investigated approach for construction of the chaotic Clapp oscillator, which can be further verified experimentally using microstrip technology.
- [10] arXiv:2605.12900 (替换) [中文pdf, pdf, html, 其他]
-
标题： Whitham调制方程用于具有三次非线性的正则化Boussinesq方程标题： Whitham modulation equations for the regularized Boussinesq equation with cubic nonlinearity评论： 43页，14图主题： 模式形成与孤子 (nlin.PS) ; 材料科学 (cond-mat.mtrl-sci)
一个正则化的Boussinesq方程被研究作为Fermi-Pasta-Ulam格子在一般三次相互作用力下的色散、长波（准连续体）近似。 以雅可比椭圆函数表示的显式周期行波解被分类，并获得了它们的孤立波、拐波和三角函数极限。 使用平均变分原理推导出描述周期行波解缓慢调制的Whitham调制方程。 对所得的流体动力学类型方程的凸性（严格双曲性、真实非线性）在一般情况下进行数值分析，并在孤立波和谐波极限情况下进行解析分析。 特别是，显示出双曲性的丧失和复共轭特征速度的形成会导致周期行波的调制不稳定性。 通过周期行波的线性化谱的数值计算以及初始值问题验证了调制不稳定的出现，这些计算还揭示了额外的短波不稳定性。
A regularized Boussinesq equation is studied as a dispersive, long-wave (quasicontinuum) approximation of the Fermi-Pasta-Ulam lattice with a general cubic interaction force. Explicit periodic traveling wave solutions in terms of Jacobi elliptic functions are classified, and their solitary-wave, kink, and trigonometric limits are obtained. The Whitham modulation equations describing slow modulations of periodic traveling wave solutions are derived using an averaged variational principle. The convexity (strict hyperbolicity, genuine nonlinearity) of the resulting hydrodynamic-type equations is examined numerically in general and analytically in the solitary-wave and harmonic limits. In particular, the loss of hyperbolicity and the formation of complex conjugate characteristic speeds is shown to lead to modulational instability of periodic traveling waves. The onset of modulational instability is verified by numerical computations of linearized spectra for periodic traveling waves and initial value problems that also reveal additional short-wave instabilities.
- [11] arXiv:2605.13379 (替换) [中文pdf, pdf, html, 其他]
-
标题： 非均匀细胞自动机在平移不变格点上的通用设计与物理应用标题： Universal Design and Physical Applications of Non-Uniform Cellular Automata on Translationally Invariant Lattices评论： 由于长度限制，摘要的完整版本可在PDF中找到。自arXiv:2401.00505和2508.13961以来的细胞自动机系列主题： 量子物理 (quant-ph) ; 强关联电子 (cond-mat.str-el) ; 形式语言与自动机理论 (cs.FL) ; 细胞自动机与格子气体 (nlin.CG)
格子几何深刻地影响了如子系统对称性和定向渗流（DP）等物理现象。在各种格子几何中，双曲格子具有常负曲率和非阿贝尔平移对称性，为研究这种几何与物理的相互作用提供了丰富的平台。然而，指数增长的格子规模和非平凡的平移对称性使得适用于欧几里得格子的方法不兼容，这一限制在均匀细胞自动机（CA）中尤为明显。为了解决这个问题，我们开发了一种适用于平移不变的规则欧几里得和双曲格子的高阶非均匀细胞自动机（NUCA）算法。在该算法中，非均匀更新规则通过一个格子变形过程包含非平凡的几何数据。我们通过在双曲$\{5,4\}$格子上的几个应用展示了该算法在双曲格子上的广泛适用性。通过应用线性 NUCA，我们生成了由子系统对称性保护的拓扑（SSPT）态以及与常规或不规则子系统对称性相关的自发子系统对称性破缺态，这些在欧几里得格子上无法实现。我们设计了多点奇异关联函数来检测非平凡的 SSPT 态，并推导了非阿贝尔平移不变 NUCA 生成模型的充分条件。此外，通过将 NUCA 扩展到非均匀 Clifford 量子细胞自动机（CQCA），我们生成了双曲簇态的子系统对称性，扩展了平移不变 CQCA 与子系统对称性之间的已知对应关系。此外，我们通过继承格子树状结构的概率性 NUCA 模拟了 DP 过程，并数值估计了渗流阈值和相图。
Lattice geometry profoundly shapes physical phenomena such as subsystem symmetry and directed percolation (DP). Among various lattice geometries, hyperbolic lattices are characterized by constant negative curvature and non-Abelian translation symmetry, offering a rich platform for investigating this geometry-physics interplay. However, the exponentially growing lattice size and nontrivial translation symmetry make approaches developed for Euclidean lattices incompatible, a limitation particularly evident in uniform cellular automata (CA). To resolve this, we develop a higher-order non-uniform cellular automata (NUCA) algorithm applicable to both translationally invariant regular Euclidean and hyperbolic lattices. In the algorithm, the non-uniform update rules incorporate nontrivial geometric data through a lattice-deforming procedure. We demonstrate the broad applicability of our algorithm to hyperbolic lattices through several applications on the hyperbolic $\{5,4\}$ lattice. By applying a linear NUCA, we generate subsystem symmetry-protected topological (SSPT) states and spontaneous subsystem symmetry-breaking states associated with regular or irregular subsystem symmetries unattainable on Euclidean lattices. We design the multi-point strange correlators to detect nontrivial SSPT states and derive a sufficient condition for non-Abelian translationally invariant NUCA-generated models. Furthermore, by generalizing the NUCA to non-uniform Clifford quantum cellular automata (CQCA), we generate subsystem symmetries of the hyperbolic cluster state, extending the established correspondence between translationally invariant CQCA and subsystem symmetries. Moreover, we simulate the DP process via a probabilistic NUCA that inherits the treelike structure of the lattice, and numerically estimate percolation thresholds and the phase diagram.
- [12] arXiv:2507.16432 (替换) [中文pdf, pdf, html, 其他]
-
标题： 多边形动力学中的坍缩标题： Collapsing in polygonal dynamics评论： 40页，7图主题： 动力系统 (math.DS) ; 精确可解与可积系统 (nlin.SI)
我们将多边形动力学定义为作用于射影空间点上的动力系统族。 最著名的例子是五角星映射。 似乎在这些系统中的大多数都出现了类似的坍缩现象。 我们在某些情况下证明了这一点，并猜想几乎总是会发生。 此外，我们给出了极限点的公式，该公式以$d+1$次多项式的根为形式（其中$d$是射影空间的维数）。 我们通过推广被解释为无穷小单值群的 Glick 算子来实现这一点。 这回答了关于其在许多系统中重新出现以及保持量的问题。 我们将这些结果应用于$\mathbb{P}^1$中的几种多边形动力学，并引入了一种新的称为“阶梯”交叉比动力学，我们对其特定配置进行了研究。
We define polygonal dynamics as a family of dynamical systems acting on points in projective spaces. The most famous example is the pentagram map. Similar collapsing phenomena seem to occur in most of these systems. We prove it in some case, and conjecture that it almost always happens. Moreover, we give a formula for the limit point in term of roots of $d+1$ degree polynomials (where $d$ is the dimension of the projective space). We do so by generalizing Glick's operator, interpreted as an infinitesimal monodromy. This answers questions about its reappearance in many systems, together with preserved quantities. We apply these results to several polygonal dynamics in $\mathbb{P}^1$ and introduce a new one called ``staircase'' cross-ratio dynamics, for which we study particular configurations.
- [13] arXiv:2507.03764 (替换) [中文pdf, pdf, html, 其他]
-
标题： 驱动耗散腔中准周期吸引子的通用量子熔化标题： Universal quantum melting of quasiperiodic attractors in driven-dissipative cavities评论： 14页，5幅图，欢迎提出意见期刊参考： 物理评论A 113，052208（2026）主题： 量子物理 (quant-ph) ; 中尺度与纳米尺度物理 (cond-mat.mes-hall) ; 适应性与自组织系统 (nlin.AO) ; 混沌动力学 (nlin.CD)
非线性经典力学已经确立了丰富的现象。 这些包括由支持不同频率先的准周期运动的环面吸引子定义的极限环面。 我们使用两个耦合的驱动耗散Kerr腔，通过Lindblad主方程进行建模，研究这种结构在开放量子系统中的命运。 结合Liouvillian谱理论与截断Wigner近似，我们表征了量子到经典的转换。 在经典极限下，两个纯虚数Liouvillian本征值表明持续的准周期模式。 量子涨落给这些本征值引入了小的负实部，导致有限的寿命，并引发环面的量子熔化。 相关的Liouvillian间隙在经典极限下代数地消失，表明具有时间平移对称性自发破缺的动力学临界转换。 量子轨迹分析显示，这种熔化是由涨落引起的去相位驱动的。 使用基于圆方差的序参量，我们揭示了系统尺寸和时间的普遍标度。 这些结果将极限环面的量子熔化确立为一种独特且稳健的非平衡临界现象，在束缚离子和超导电路中有明确的实验特征。
Nonlinear classical mechanics has established rich phenomena. These include limit tori defined by toroidal attractors supporting quasiperiodic motion with incommensurate frequencies. We study the fate of such structures in open quantum systems using two coupled driven-dissipative Kerr cavities modeled via the Lindblad master equation. Combining Liouvillian spectral theory with the truncated Wigner approximation, we characterize the quantum-to-classical crossover. In the classical limit, two pairs of purely imaginary Liouvillian eigenvalues signal persistent quasiperiodic modes. Quantum fluctuations induce small negative real parts to these eigenvalues, giving rise to finite lifetimes and leading to the quantum melting of the torus. The associated Liouvillian gaps vanish algebraically in the classical limit, indicating a dynamical critical crossover with spontaneous breaking of time-translational symmetry. Quantum trajectory analysis reveals that this melting is driven by fluctuation-induced dephasing. Using a circular-variance-based order parameter, we uncover universal scaling in system size and time. These results establish quantum melting of limit tori as a distinct and robust non-equilibrium critical phenomenon, with clear experimental signatures in trapped ions and superconducting circuits.
- [14] arXiv:2107.00095 (替换) [中文pdf, pdf, html, 其他]
-
标题： 维数相关的Brunn-Minkowski不等式中的一种普遍界限 for 对数凹测度标题： A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures评论： 19页；这是最初作为arXiv:2103.11433的一部分，但该论文被分成了两篇论文。2026年5月对表述进行了小的更正。即对命题4.2和定理A证明开头的论证进行了小的修改。主题： 度量几何 (math.MG) ; 偏微分方程分析 (math.AP) ; 概率 (math.PR)
我们证明了对于 $μ$ 上的任何对数凹测度， $\mathbb{R}^n$ 上的任何一对对称凸集 $K$ 和 $L$，以及任何 $λ\in [0,1],$ $$μ((1-λ) K+λL)^{c_n}\geq (1-λ) μ(K)^{c_n}+λμ(L)^{c_n},$$ 其中 $c_n\geq n^{-4-o(1)}.$ 这是对维数 Brunn-Minkowski 猜想的进展（参见 Gardner, Zvavitch \cite{GZ}，Colesanti, L, Marsiglietti \cite{CLM}）。 此外，我们的界对于各种特殊的对数凹测度类有所改进。
We show that for any log-concave measure $μ$ on $\mathbb{R}^n$, any pair of symmetric convex sets $K$ and $L$, and any $λ\in [0,1],$ $$μ((1-λ) K+λL)^{c_n}\geq (1-λ) μ(K)^{c_n}+λμ(L)^{c_n},$$ where $c_n\geq n^{-4-o(1)}.$ This constitutes progress towards the dimensional Brunn-Minkowski conjecture (see Gardner, Zvavitch \cite{GZ}, Colesanti, L, Marsiglietti \cite{CLM}). Moreover, our bound improves for various special classes of log-concave measures.