非线性科学
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- [1] arXiv:2508.05270 [中文pdf, pdf, html, 其他]
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标题： 从变形的D$_4$丛代数得到的可交换可积映射标题： Commuting integrable maps from a deformed D$_4$ cluster algebra主题： 精确可解与可积系统 (nlin.SI) ; 数学物理 (math-ph)
在本文中，我们重新研究了一个平面可积映射，该映射最近作为D型簇代数的变形突变的两参数族获得，记为$_4$。 该映射的有理首次积分定义了由水平曲线构成的平面不变叶状结构，我们解释了这如何对应于一个秩为2的有理椭圆曲面。 这使我们构造了另一个（独立的）可积映射，与第一个映射对易，且这两个映射都可以提升为在一个扩展簇代数中的突变复合，其基础箭图与Okubo为$q$- Painlevé VI方程找到的箭图等价。 两个对易映射的度增长以两种不同方式计算：首先，从簇变量的d向量的热带（max-plus）方程；其次，通过将$\mathbb{P}^1 \times \mathbb{P}^1$进行爆破来构建两个映射的初始条件最小空间。
In this paper we revisit an integrable map of the plane which we obtained recently as a two-parameter family of deformed mutations in the cluster algebra of type D$_4$. The rational first integral for this map defines an invariant foliation of the plane by level curves, and we explain how this corresponds to a rational elliptic surface of rank 2. This leads us to construct another (independent) integrable map, commuting with the first, such that both maps lift to compositions of mutations in an enlarged cluster algebra, whose underlying quiver is equivalent to the one found by Okubo for the $q$-Painlev\'e VI equation. The degree growth of the two commuting maps is calculated in two different ways: firstly, from the tropical (max-plus) equations for the d-vectors of the cluster variables; and secondly, by constructing the minimal space of initial conditions for the two maps, via blowing up $\mathbb{P}^1 \times \mathbb{P}^1$.
新提交 (展示 1 之 1 条目 )
- [2] arXiv:2508.04763 (交叉列表自 cond-mat.str-el) [中文pdf, pdf, html, 其他]
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标题： 大量不稳定的周期轨道和高度受挫磁体中的量子超聚焦标题： Unstable periodic orbits galore and quantum hyperscarring in highly frustrated magnets评论： 5 + 2页，3 + 2图主题： 强关联电子 (cond-mat.str-el) ; 混沌动力学 (nlin.CD) ; 量子物理 (quant-ph)
高度受挫的磁体，因其宏观简并的经典基态和大量纠缠的量子自旋液体相，对于现代凝聚态概念的发展至关重要，如涌现对称性、拓扑序和分数化。 在高能区域，由于多体动力学变得混沌，受挫和大量简并效应至今研究较少。 在这里，我们识别出一种高能动态类比的高度受挫磁性，表现为一个广泛的经典“相互作用抑制”配置流形，导致不稳定的周期轨道。 这些周期轨道通常既不被对称性保护，也不可积，它们来源于一组动力学局部约束，这些约束有效地消除了相互作用，同时允许广泛数量的局部自由度。 在量子情况下，不稳定周期轨道的大量存在对应于“超疤痕”，即在指数级多的不稳定周期轨道上的量子疤痕。 在后者的产物态上，中谱热态的振幅表现出幂律分布，这与通用产物态所预期的指数波特-托马斯分布形成鲜明对比。 我们的结果揭示了一个新的受限动力学区域，在该区域内，多体量子混沌与结构化的相干动力学流形共存，并建立了一个此前难以捉摸的广泛疤痕机制。
Highly frustrated magnets, with their macroscopically-degenerate classical ground states and massively-entangled quantum spin liquid phases, have been pivotal to the development of modern condensed matter concepts such as emergent symmetries, topological order, and fractionalisation. The effects of frustration and massive degeneracies at high energy, where the many-body dynamics becomes chaotic, have hitherto been far less explored. Here, we identify a high-energy dynamical analog of highly-frustrated magnetism, in the form of an extensive manifold of classical ''interaction-suppressing'' configurations giving rise to unstable periodic orbits. These are in general neither protected by symmetry nor integrability, and emerge from a set of dynamical local constraints that effectively nullify the interactions while allowing extensively many local degrees of freedom. The proliferation of unstable periodic orbits corresponds in the quantum case to ''hyperscarring'', that is, quantum scarring on exponentially many unstable periodic orbits. On the product states associated to the latter, the amplitudes of the mid-spectrum thermal eigenstates exhibit a power-law distribution, in stark contrast to the expected exponential Porter-Thomas distribution that holds for generic product states. Our results reveal a new constrained dynamical regime where many-body quantum chaos coexists with structured manifolds of coherent dynamics, and establishes a mechanism for hitherto elusive extensive scarring.
- [3] arXiv:2508.04983 (交叉列表自 cond-mat.stat-mech) [中文pdf, pdf, html, 其他]
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标题： 随机循环神经网络中的动能标题： Kinetic energy in random recurrent neural networks评论： 8页，6图主题： 统计力学 (cond-mat.stat-mech) ; 混沌动力学 (nlin.CD) ; 神经与认知 (q-bio.NC)
不稳定固定点与高维神经动力学中的混沌动力学之间的关系仍然不明确。 在本工作中，我们通过将动力学平均场理论与大量数值模拟相结合，研究了随机循环神经网络的动能分布。 我们发现，在耦合方差（突触增益）的关键值处，平均动能从零连续地转移到正值，并且在临界点附近表现出幂律行为。 通过理论进一步计算了稳态活动分布，并与有限尺寸系统的模拟进行了比较。 这项研究为理解动能的景观提供了第一步，这可能反映了非平衡动力学相空间的结构。
The relationship between unstable fixed points and chaotic dynamics in high-dimensional neural dynamics remains elusive. In this work, we investigate the kinetic energy distribution of random recurrent neural networks by combining dynamical mean-field theory with extensive numerical simulations. We find that the average kinetic energy shifts continuously from zero to a positive value at a critical value of coupling variance (synaptic gain), with a power-law behavior close to the critical point. The steady-state activity distribution is further calculated by the theory and compared with simulations on finite-size systems. This study provides a first step toward understanding the landscape of kinetic energy, which may reflect the structure of phase space for the non-equilibrium dynamics.
- [4] arXiv:2508.05288 (交叉列表自 q-bio.NC) [中文pdf, pdf, html, 其他]
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标题： 非线性循环神经网络中的协方差谱标题： Covariance spectrum in nonlinear recurrent neural networks评论： 33页，9图主题： 神经与认知 (q-bio.NC) ; 混沌动力学 (nlin.CD)
随着对大量神经元同时记录技术的进步，人们对神经种群活动的结构（如维度）产生了浓厚的兴趣。一个关键问题是这些动态特征是如何通过机制产生的，以及它们与电路连接的关系。之前曾提出使用协方差特征值分布（或谱），这在随机递归网络中可以解析推导，作为描述神经种群活动形状的稳健度量，超越了维度（Hu和Sompolinsky 2022）。理论谱的应用广泛地发现了与实验数据的准确匹配，为观察到的低维种群动态提供了机制见解（Morales等 2023）。然而，实证成功突显了理论上的一个空白，因为用于推导谱的神经网络模型是简化的，具有线性神经元。在这项工作中，我们旨在通过研究具有非线性神经元的网络中的协方差谱，并在包括混沌在内的更广泛的动态条件下进行研究，来填补这一空白。令人惊讶的是，我们发现谱可以通过类似于线性理论的方程精确理解，但用一个有效递归连接强度参数代替，该参数反映了连接权重和神经元的非线性。在不同的动态条件下，这个有效连接强度为谱和维度的变化提供了一个统一的解释，并在混沌条件下保持接近临界值而无需微调。这些结果进一步加深了我们对非线性神经种群动态的理解，并为在生物电路中应用协方差谱分析提供了额外的理论支持。
Advances in simultaneous recordings of large numbers of neurons have driven significant interest in the structure of neural population activity such as dimension. A key question is how these dynamic features arise mechanistically and their relationship to circuit connectivity. It was previously proposed to use the covariance eigenvalue distribution, or spectrum, which can be analytically derived in random recurrent networks, as a robust measure to describe the shape of neural population activity beyond the dimension (Hu and Sompolinsky 2022). Applications of the theoretical spectrum have broadly found accurate matches to experimental data across brain areas providing mechanistic insights into the observed low dimensional population dynamics (Morales et al. 2023). However, the empirical success highlights a gap in theory, as the neural network model used to derive the spectrum was minimal with linear neurons. In this work, we aim to close this gap by studying the covariance spectrum in networks with nonlinear neurons and under broader dynamical regimes including chaos. Surprisingly, we found that the spectrum can be precisely understood by equations analogous to the linear theory substituted with an effective recurrent connection strength parameter, that reflects both the connection weights and the nonlinearity of neurons. Across dynamical regimes, this effective connection strength provides a unified interpretation for the spectrum and dimension changes, and stays near the critical value in the chaotic regime without fine-tuning. These results further our understanding of nonlinear neural population dynamics and provide additional theoretical support for applying the covariance spectrum analysis in biological circuits.
- [5] arXiv:2508.05346 (交叉列表自 quant-ph) [中文pdf, pdf, html, 其他]
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标题： 湍流场的几何量子编码标题： Geometric quantum encoding of a turbulent field主题： 量子物理 (quant-ph) ; 混沌动力学 (nlin.CD) ; 流体动力学 (physics.flu-dyn)
多尺度系统的混沌结构对其量子编码提出了严峻的挑战。 我们提出了一种三阶段超球面编码方法用于湍流场。 该方法包括对基态的对称性保持扰动、特定测量的卷积以及可观测量的最终反卷积。 后两个阶段利用Hopf纤维化将量子可观测量映射到涡管上，这些是流体湍流的基本构建块。 使用27个量子位，我们生成了一个雷诺数为$\mathit{Re} = 13900$的瞬时湍流场，该场再现了具有Kolmogorov五分之三次幂谱的能谱、纠缠的涡旋结构和强间歇性。 该方法仅需要$\mathcal{O}(\log_2\mathit{Re})$个量子位，这对于湍流场编码来说在渐近意义上是最优的。 这相对于经典方法实现了指数级的记忆缩减，并实现了大规模多尺度系统量子模拟的状态制备。
The chaotic structure of multiscale systems presents a formidable challenge to their quantum encoding. We propose a three-stage hyperspherical encoding method for turbulent fields. This method comprises a symmetry-preserving perturbation of the ground state, a measurement-specific convolution, and a final deconvolution of observables. The latter two stages employ the Hopf fibration to map quantum observables onto vortex tubes, the building blocks of fluid turbulence. Using 27 qubits, we generate an instantaneous turbulent field at a Reynolds number of $\mathit{Re} = 13900$ that reproduces the energy spectrum with Kolmogorov's five-thirds scaling, tangled vortex structures, and strong intermittency. The method only requires $\mathcal{O}(\log_2\mathit{Re})$ qubits, which is asymptotically optimal for turbulent-field encoding. This yields an exponential memory reduction over classical methods, and enables state preparation for large-scale quantum simulation of multiscale systems.
- [6] arXiv:2508.05619 (交叉列表自 cs.AI) [中文pdf, pdf, html, 其他]
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标题： 缺失的奖励：经验时代的主动推理标题： The Missing Reward: Active Inference in the Era of Experience主题： 人工智能 (cs.AI) ; 适应性与自组织系统 (nlin.AO) ; 生物物理 (physics.bio-ph) ; 计算物理 (physics.comp-ph) ; 物理的历史与哲学 (physics.hist-ph)
本文认为，主动推理（AIF）为开发能够从经验中学习而无需持续人类奖励工程的自主AI代理提供了关键基础。 随着AI系统开始耗尽高质量训练数据，并依赖越来越大的人力资源进行奖励设计，当前范式面临严重的可扩展性挑战，这可能会阻碍真正自主智能的发展。 提出一个“经验时代”的设想，其中代理从自生成的数据中学习，这是一个有希望的进展。 然而，这一愿景仍然依赖于对奖励函数的大量人工工程，实际上将瓶颈从数据整理转移到了奖励整理。 这突显了我们所识别的\textbf{基础能动性差距}：当代AI系统在应对变化情况时无法自主制定、适应和追求目标的能力。 我们认为AIF可以通过用内在的最小化自由能驱动取代外部奖励信号，来填补这一差距，使代理通过统一的贝叶斯目标自然地平衡探索与利用。 通过将大型语言模型作为生成世界模型与AIF的原则性决策框架相结合，我们可以创建能够高效从经验中学习同时保持与人类价值观一致的代理。 这种综合方法为AI系统提供了一条有说服力的路径，使其能够在遵循计算和物理约束的同时自主发展。
This paper argues that Active Inference (AIF) provides a crucial foundation for developing autonomous AI agents capable of learning from experience without continuous human reward engineering. As AI systems begin to exhaust high-quality training data and rely on increasingly large human workforces for reward design, the current paradigm faces significant scalability challenges that could impede progress toward genuinely autonomous intelligence. The proposal for an ``Era of Experience,'' where agents learn from self-generated data, is a promising step forward. However, this vision still depends on extensive human engineering of reward functions, effectively shifting the bottleneck from data curation to reward curation. This highlights what we identify as the \textbf{grounded-agency gap}: the inability of contemporary AI systems to autonomously formulate, adapt, and pursue objectives in response to changing circumstances. We propose that AIF can bridge this gap by replacing external reward signals with an intrinsic drive to minimize free energy, allowing agents to naturally balance exploration and exploitation through a unified Bayesian objective. By integrating Large Language Models as generative world models with AIF's principled decision-making framework, we can create agents that learn efficiently from experience while remaining aligned with human values. This synthesis offers a compelling path toward AI systems that can develop autonomously while adhering to both computational and physical constraints.
交叉提交 (展示 5 之 5 条目 )
- [7] arXiv:2502.01782 (替换) [中文pdf, pdf, html, 其他]
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标题： 风生海洋环流的可变性拓扑模式标题： Topological modes of variability of the wind-driven ocean circulation评论： 23页，20图主题： 混沌动力学 (nlin.CD)
拓扑复形是编码相空间中流分支结构的拓扑对象。 我们基于这些对象引入了可变性拓扑模式（TMVs）的概念。 TMVs 被定义为在拓扑复形中代数定义的循环，称为生成元，它们提供了抽象拓扑不变量与模型或观测中的时间依赖行为之间的具体联系。 我们将这种方法应用于一个受周期性和非周期性强迫影响的风驱动海洋环流的低阶模型，并展示了 TMVs 在非自治环境中如何随时间出现或消失。 分析表明，TMVs 使得对复杂系统中可变性的理解有了定性的新视角，在这些系统中线性模式无法描述非线性动力学。
Templexes are topological objects that encode the branching organization of a flow in phase space. We build on these objects to introduce the concept of topological modes of variability (TMVs). TMVs are defined as dynamical manifestations of algebraically defined cycles, called generatexes, in the templex; they provide a concrete link between abstract topological invariants and time-dependent behavior in a model or in observations. We apply this approach to a low-order model of the wind-driven ocean circulation, subject to both periodic and aperiodic forcing, and show how TMVs emerge or vanish over time in nonautonomous settings. The analysis reveals that TMVs allow for a qualitatively new understanding of variability in complex systems where linear modes fail to describe the nonlinear dynamics.
- [8] arXiv:2506.06639 (替换) [中文pdf, pdf, html, 其他]
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标题： 随机梯度下降校准用于混沌抑制的Sprott电路Pyragas延迟反馈控制标题： Stochastic Gradient-Descent Calibration of Pyragas Delayed-Feedback Control for Chaos Suppression in the Sprott Circuit评论： 10个图表主题： 混沌动力学 (nlin.CD) ; 优化与控制 (math.OC) ; 计算物理 (physics.comp-ph)
本文探讨了通过利用随机梯度下降（SGD）校准Pyragas延迟反馈控制来实现Sprott电路中的混沌控制。使用一个三阶非线性微分方程，我们对电路进行建模，并旨在通过优化控制参数（增益$K$，延迟$T_{\text{con}}$）和可变电阻$R_v$来抑制混沌。从已发表的图表中通过WebPlotDigitizer提取的实验电压数据作为校准目标。我们比较了两种校准技术：通过网格搜索进行平方误差和（SSE）最小化和使用有限差分的随机梯度下降（SGD）。使用SGD对$K$、$T_{\text{con}}$和$R_v$进行联合优化，实现了与实验数据更一致的匹配，高保真地捕捉了相位和振幅。与网格搜索相比，SGD在相位同步方面表现更优，但由于模型简化，仍存在轻微的振幅差异。相空间分析证实了模型能够复制混沌吸引子的几何形状，尽管存在轻微偏差。我们分析了校准精度与计算成本之间的权衡，突出了可扩展性挑战。总体而言，基于SGD的校准展示了在精确控制混沌系统方面的显著潜力，推动了数学建模在电气工程中的应用。
This paper explores chaos control in the Sprott circuit by leveraging Stochastic Gradient Descent (SGD) to calibrate Pyragas delayed feedback control. Using a third-order nonlinear differential equation, we model the circuit and aim to suppress chaos by optimizing control parameters (gain $K$, delay $T_{\text{con}}$) and the variable resistor $R_v$. Experimental voltage data, extracted from published figures via WebPlotDigitizer, serve as the calibration target. We compare two calibration techniques: sum of squared errors (SSE) minimization via grid search and stochastic gradient descent (SGD) with finite differences. Joint optimization of $K$, $T_{\text{con}}$, and $R_v$ using SGD achieves superior alignment with experimental data, capturing both phase and amplitude with high fidelity. Compared to grid search, SGD excels in phase synchronization, though minor amplitude discrepancies persist due to model simplifications. Phase space analysis confirms the model ability to replicate the chaotic attractor geometry, despite slight deviations. We analyze the trade-off between calibration accuracy and computational cost, highlighting scalability challenges. Overall, SGD-based calibration demonstrates significant potential for precise control of chaotic systems, advancing mathematical modeling and applications in electrical engineering.
- [9] arXiv:2410.06039 (替换) [中文pdf, pdf, html, 其他]
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标题： 量子增强热化标题： Quantum Enhancement of Thermalization期刊参考： 物理评论快报 135 (2025), 060404主题： 量子气体 (cond-mat.quant-gas) ; 统计力学 (cond-mat.stat-mech) ; 混沌动力学 (nlin.CD)
多体系统在具有大量自由度时的平衡性质通常预期由统计力学来描述。 这种预期与热化现象密切相关，表现为时间依赖可观测量中的能量均分，这在量子和经典系统中都会发生，但表现可能非常不同。 通过研究超冷玻色气体中单个晶格位点的种群动力学，我们表明，在量子系统中向平衡状态的弛豫过程可以比其经典对应物快几个数量级。 经典混沌量揭示了这是由于量子系统中的波包能够通过类似隧穿的机制逃离低效的经典输运区域。 由于所呈现的现象发生在广泛的参数范围内，并且在弱无序系统中仍然存在，我们预计它会在各种多体系统中出现，并且可以在最先进的量子模拟平台中直接进行实验验证。
Equilibrium properties of many-body systems with a large number of degrees of freedom are generally expected to be described by statistical mechanics. Such expectations are closely tied to the observation of thermalization, as manifested through equipartition in time-dependent observables, which takes place both in quantum and classical systems but may look very different in comparison. By studying the dynamics of individual lattice site populations in ultracold bosonic gases, we show that the process of relaxation toward equilibrium in a quantum system can be orders of magnitude faster than in its classical counterpart. Classical chaos quantifiers reveal that this is due to a wave packet in a quantum system being able to escape regions of inefficient classical transport by a mechanism akin to tunneling. Since the presented phenomenon takes place in a broad parameter range and persists in weakly disordered systems, we expect that it occurs in a variety of many-body systems and is amenable to direct experimental verification in state-of-the-art quantum simulation platforms.
- [10] arXiv:2502.11296 (替换) [中文pdf, pdf, html, 其他]
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标题： 活性固体：无流动的拓扑缺陷自推进标题： Active Solids: Topological Defect Self-Propulsion Without Flow评论： 9页，4图；v2：修订了引言和讨论主题： 软凝聚态物理 (cond-mat.soft) ; 模式形成与孤子 (nlin.PS)
+1/2拓扑缺陷的自推进是活性向列流体的特征，其中缺陷被它们自身产生的流场带动。 在本文中，我们提出了一个用于向列活性固体中缺陷自推进的最小模型：一种嵌入了生成主动应力和相关弹性应变的向列纹理的线性弹性介质。 我们证明，这种耦合会产生相对于弹性介质移动的自推进+1/2缺陷，这是通过局部重塑向列纹理而无需对流实现的。 这一机制与流体情况根本不同，可能导致缺陷对的解离和+1缺陷的稳定。 我们的发现可能有助于解释例如肌肉纤维的取向序在固态组织形态发生过程中是如何重新配置的。 该提出的机制可能控制+1/2缺陷的运动和融合，这些缺陷在水螅再生期间建立身体轴中起着关键作用。
The self-propulsion of +1/2 topological defects is a hallmark of active nematic fluids, where the defects are advected by the flow field they themselves generate. In this paper we propose a minimal model for defect self-propulsion in a nematic active solid: a linear elastic medium with an embedded nematic texture that generates active stress and associated elastic strains. We show that such coupling gives rise to self-propelled +1/2 defects that move relative to the elastic medium by local remodeling of the nematic texture without advection. This mechanism is fundamentally different from the fluid case and can lead to unbinding of defect pairs and stabilization of +1 defects. Our findings might help explain how orientational order, of, for example, muscle fibers, is reconfigured during morphogenesis in solid-like tissues. The proposed mechanism may, for instance, control motility and merging of +1/2 defects, which play a crucial role in setting up the body axis during Hydra regeneration.
- [11] arXiv:2503.13767 (替换) [中文pdf, pdf, html, 其他]
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标题： 瑞利-泰勒、开尔文-赫姆霍兹和不可混溶到可混溶淬火不稳定性在二元玻色-爱因斯坦凝聚体中标题： Rayleigh-Taylor, Kelvin-Helmholtz and immiscible to miscible quenching instabilities in binary Bose-Einstein condensates评论： 26页，14图，附带4个mp4文件主题： 量子气体 (cond-mat.quant-gas) ; 模式形成与孤子 (nlin.PS) ; 量子物理 (quant-ph)
我们研究了在二元不混溶均匀玻色-爱因斯坦凝聚体中三种类型的不稳定性，考虑的是铷同位素$^{85}$Rb 和$^{87}$Rb 被限制在二维圆形盒子中。 在强扰动下研究了瑞利-泰勒（RT）和开尔文-赫姆霍兹（KH）不稳定性类型。 在没有外部扰动的情况下，通过不混溶到混溶淬火转变（IMQT）探测不稳定性，采用两种不同的初始配置。 我们的数值模拟显示，所有这些不稳定性动力学都由大涡旋生成和声波（声子）传播主导。 对于长期传播，涡旋动力学在 KH 不稳定性中超过声波，而在其他情况下声波激发占主导地位。 对于所有动态模拟，研究了动能谱的可压缩和不可压缩部分可能的标度定律，根据波数$k$。 相应的结果与经典柯尔莫哥洛夫标度$k^{-5/3}$和$k^{-3}$进行了比较，这些标度在某些特定时间间隔的动能谱中被观察到。 偏离经典标度，在 IMQT 谱中注意到一种“瓶颈效应”。
We investigate three kinds of instabilities in binary immiscible homogeneous Bose-Einstein condensate, considering rubidium isotopes $^{85}$Rb and $^{87}$Rb confined in two-dimensional circular box. Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) instability types are studied under strong perturbations. Without external perturbation, instabilities are also probed by immiscible to miscible quenching transition (IMQT), under two different initial configurations. Our numerical simulations show that all such instability dynamics are dominated by large vortex productions and sound-wave (phonon) propagations. For long-term propagation, vortex dynamics become dominant over sound waves in the KH instability, while sound wave excitations predominate in the other cases. For all the dynamical simulations, the emergence of possible scaling laws are investigated for the compressible and incompressible parts of the kinetic energy spectra, in terms of the wave number $k$. The corresponding results are compared with the classical Kolmogorov scalings, $k^{-5/3}$ and $k^{-3}$, for turbulence, which are observed in the kinetic energy spectra at some specific time intervals. Deviating from the classical scaling, a kind of ``Bottleneck effect" is noticed in the IMQT spectra.
- [12] arXiv:2504.06360 (替换) [中文pdf, pdf, html, 其他]
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标题： 极化子流体的量子流体力学：纯能量弛豫项标题： Quantum hydrodynamics of a polariton fluid: pure energy relaxation terms评论： 6页 + 4页的补充材料主题： 中尺度与纳米尺度物理 (cond-mat.mes-hall) ; 模式形成与孤子 (nlin.PS) ; 量子物理 (quant-ph)
腔极化子是在强耦合 regime 中量子微腔中的混合半光半物质激发，表现出清晰的量子集体行为特征，例如在显著高温下的玻色-爱因斯坦凝聚体和超流性的类比现象。 这些状态的形成分析需要考虑系统中的弛豫过程。 尽管有一些已建立的方法可以描述其中的一些过程，例如有限寿命的极化子、外部光学泵浦以及与非相干激子库的耦合，但对极化子流体中纯能量弛豫的处理仍然是一个谜题。 在此基础上，我们基于量子流体力学方法推导出相应的方程，其中能量弛豫项自然出现。 我们详细分析了它如何影响极化子液滴的动力学以及均匀极化子凝聚体的基本激发的色散。 虽然我们专注于腔极化子的情况，但我们的方法也可以应用于其他玻色凝聚体的情况，其中能量弛豫过程起着重要作用。
Cavity polaritons, hybrid half-light half-matter excitations in quantum microcavities in the strong-coupling regime demonstrate clear signatures of quantum collective behavior, such as analogues of Bose-Einstein condensate and superfluidity at remarkably high temperatures. The analysis of the formation of these states demands an account of the relaxation processes in the system. Although there are well-established approaches for the description of some of them, such as finite lifetime polariton, an external optical pump, and coupling with an incoherent excitonic reservoir, the treatment of pure energy relaxation in a polariton fluid still remains a puzzle. Here, based on the quantum hydrodynamics approach, we derive the corresponding equations where the energy relaxation term appears naturally. We analyze in detail how it affects the dynamics of polariton droplets and the dispersion of elementary excitations of a uniform polariton condensate. Although we focus on the case of cavity polaritons, our approach can be applied to other cases of bosonic condensates, where the processes of energy relaxation play an important role.
- [13] arXiv:2507.09849 (替换) [中文pdf, pdf, html, 其他]
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标题： 紧密束缚库珀对超导体中阿布里科索夫涡旋核心外超导性的增强标题： Enhancement of superconductivity outside Abrikosov vortex core in a tightly bound Cooper pair superconductor评论： 10页，2图主题： 超导性 (cond-mat.supr-con) ; 模式形成与孤子 (nlin.PS)
阿布里科索夫涡旋在II型超导体中破坏超导性起着核心作用。 人们普遍认为，当远离$s$波超导体的涡旋轴时，超导电子的密度从零逐渐增加到其体值。 然而，我们证明，如果构成超导液体的库珀对结合得足够紧密，那么在零温度极限下，这种行为会发生定性变化。 具体来说，在涡旋核心之外，超导电子的密度达到一个超过其体值的最大值。 这一现象具有静电起源：由于正常电子缺失，并存在带电的离子背景，超导电子电荷密度的空间变化会破坏局部电中性，从而产生电场。 这个电场缩小了涡旋核心，并使密度分布变为具有最大值的形式，确保全局电中性。 在强静电屏蔽极限下，该效应最为明显，此时描述涡旋的场配置呈现出一种普遍形式，电场在由伦敦穿透深度决定的长度尺度上被屏蔽。
Abrikosov vortices play a central role in the disruption of superconductivity in type-II superconductors. It is commonly accepted that as one moves away from the vortex's axis of an $s$-wave superconductor, the density of superconductive electrons gradually increases from zero to its bulk value. However, we demonstrate that this behavior is qualitatively altered in the zero-temperature limit provided that the Cooper pairs comprising the superconductive liquid are sufficiently tightly bound. Specifically, outside the vortex core, the density of superconductive electrons reaches a maximum surpassing its bulk value. This phenomenon has electrostatic origins: since normal electrons are absent and there exists a charged ionic background, the spatial variation of the charge density of superconductive electrons violates local neutrality, leading to the generation of an electric field. This electric field shrinks the vortex core and turns the density profile into that with a maximum, ensuring global neutrality. The effect is most pronounced in the limit of strong electrostatic screening, where the field configurations describing the vortex attain a universal form, with the electric field screened over a length scale determined by the London penetration depth.