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Transmission across a ribbon containing a square PT impurity 在含有方形 PT 杂质的色带上的传输
Pub Date : 2024-03-20 DOI: arxiv-2403.13217
Cristian Mejía-Cortés, Mario I. Molina
We study the spectrum and transmission coefficient of plane waves propagatingalong square ribbons of varying widths, containing a square-shaped,PT-symmetric impurity region. We start with a zero-width ribbon (1D chain) andplace a PT symmetric dimer. The spectrum is computed numerically and theinstability gain is computed as a function of the gain/loss dimer strength. Thetransmission coefficient is obtained in closed form and examined as a functionof wavevector and the gain/loss parameter. Next, we study a ribbon in a narrowladder configuration containing a square PT impurity. As before, we compute theinstability gain numerically and the transmission coefficient in closed formfor the two possible input modes. Finally, we repeat the calculations for awider ladder ribbon containing a Lieb-like impurity in a PT configuration. Forall cases and transmission channels, we obtain transmission divergences inwavevector-gain/loss parameter space, whose number increases with the width ofthe ribbon
我们研究了沿着不同宽度的方形带传播的平面波的频谱和透射系数,其中包含一个方形的 PT 对称杂质区。我们从零宽度带(一维链)开始,然后放置一个 PT 对称二聚体。光谱是通过数值计算得出的,而不稳定性增益则是作为增益/损耗二聚体强度的函数计算得出的。传输系数以封闭形式获得,并作为波矢和增益/损耗参数的函数进行检验。接下来,我们研究了含有方形 PT 杂质的窄梯形结构色带。与之前一样,我们通过数值计算不稳定增益,并以闭合形式计算两种可能输入模式的传输系数。最后,我们重复计算了在 PT 配置中含有类李布杂质的更宽梯形带。对于所有情况和传输通道,我们都得到了波矢增益/损耗参数空间中的传输发散,其数量随着阶梯带宽度的增加而增加
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引用次数: 0
Two-level systems and harmonic excitations in a mean-field anharmonic quantum glass 均场非谐波量子玻璃中的两级系统和谐波激发
Pub Date : 2024-03-19 DOI: arxiv-2403.12740
Thibaud Maimbourg
Structural glasses display at low temperature a set of anomalies inthermodynamic observables. The prominent example is the linear-in-temperaturescaling of the specific heat, at odds with the Debye cubic scaling found incrystals, due to acoustic phonons. Such an excess of specific heat in amorphoussolids is thought of arising from phenomenological soft excitations dubbedtunneling two-level systems (TTLS). Their nature as well as their statisticalproperties remain elusive from a first-principle viewpoint. In this work weinvestigate the canonically quantized version of the KHGPS model, a mean-fieldglass model of coupled anharmonic oscillators, across its phase diagram, withan emphasis on the specific heat. The thermodynamics is solved in asemiclassical expansion. We show that in the replica-symmetric region of themodel, up to the marginal glass transition line where replica symmetry getscontinuously broken, a disordered version of the Debye approximation holds: thespecific heat is dominated by harmonic vibrational excitations inducing apower-law scaling at the transition, ruled by random matrix theory. Thismechanism generalizes a previous semiclassical argument in the literature. Wethen study the marginal glass phase where the semiclassical expansion becomesnon-perturbative due to the emergence of instantons that overcome disorderedDebye behavior. Inside the glass phase, a variational solution to the instantonapproach provides the prevailing excitations as TTLS, which generate a linearspecific heat. This phase thus hosts a mix of TTLS and harmonic excitationsgenerated by interactions. We finally suggest to go beyond the variationalapproximation through an analogy with the spin-boson model.
结构玻璃在低温下显示出一系列热力学观测指标的反常现象。最突出的例子是比热在温度下的线性缩放,这与晶体中发现的德拜立方缩放不同,是由声子引起的。无定形固体中的这种比热过剩被认为是由被称为隧道两级系统(TTLS)的现象学软激发引起的。从第一原理的角度来看,它们的性质及其统计特性仍然难以捉摸。在这项工作中,我们研究了 KHGPS 模型的典型量化版本--耦合非谐振子的均场玻璃模型--的整个相图,重点是比热。热力学是通过非经典扩展求解的。我们的研究表明,在该模型的复制对称区域,直到复制对称性被持续打破的边缘玻璃转变线,德拜近似的无序版本是成立的:比热由谐振激振主导,在转变过程中诱发幂律缩放,由随机矩阵理论支配。这一机制概括了之前文献中的半经典论证。我们研究了边缘玻璃相,由于瞬子的出现,半经典扩展变得非微扰,从而克服了无序Debye行为。在玻璃相内部,瞬子方法的可变解提供了作为 TTLS 的主要激元,它们会产生线性特定热。因此,这一阶段包含了 TTLS 和由相互作用产生的谐波激振的混合。最后,我们建议通过与自旋玻色子模型的类比来超越变分近似。
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引用次数: 0
Inhomogeneous Floquet thermalization 非均质 Floquet 热化
Pub Date : 2024-03-13 DOI: arxiv-2403.08369
Soumya Bera, Ishita Modak, Roderich Moessner
How a closed system thermalizes, especially in the absence of globalconservation laws but in the presence of disorder and interactions, is one ofthe central questions in non-equilibrium statistical mechanics. We explore thisfor a disordered, periodically driven Ising chain. Our numerical results revealinhomogeneous thermalization leading to a distribution of thermalizationtimescales within a single disordered sample, which we encode via adistribution of effective local temperatures. Using this, we find an excellentcollapse $textit{without}$ $textit{any}$ $textit{fitting}$$textit{parameters}$ of the local relaxation dynamics for the entire range ofdisorder values in the ergodic regime when adapting the disorder-averageddiagonal entanglement entropy as internal `time' of the system. This approachevidences a remarkably uniform parametrization of the dynamical many-bodyevolution of local temperature within the otherwise highly heterogeneousergodic regime, independent of the strength of the disorder.
封闭系统如何热化,尤其是在缺乏全局守恒定律但存在无序和相互作用的情况下,是非平衡统计力学的核心问题之一。我们针对无序、周期性驱动的伊辛链探讨了这一问题。我们的数值结果揭示了在单一无序样本中导致热化时间尺度分布的均质热化,我们通过有效局部温度的分布对其进行编码。利用这一点,当把无序平均对角线纠缠熵作为系统的内部 "时间 "时,我们发现在遍历机制的整个无序值范围内,局部弛豫动力学的 "时间尺度 "都有很好的 "坍缩"($textit{without}$ $textit{fitting}$$textit{parameters}$ )。这种方法为原本高度异质的遍历机制中局部温度的动态多体演化提供了非常统一的参数,而与无序的强度无关。
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引用次数: 0
Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations 自旋玻璃中的小场混沌:超计量树的普遍预测以及与数值模拟的比较
Pub Date : 2024-03-13 DOI: arxiv-2403.08503
Miguel Aguilar-Janita, Silvio Franz, Victor Martin-Mayor, Javier Moreno-Gordo, Giorgio Parisi, Federico Ricci-Tersenghi, Juan J. Ruiz-Lorenzo
We study the chaotic behavior of the Gibbs state of spin-glasses under theapplication of an external magnetic field, in the crossover region where thefield intensity scales proportional to $1/sqrt{N}$, being $N$ the system size.We show that Replica Symmetry Breaking (RSB) theory provides universalpredictions for chaotic behavior: they depend only on the zero-field overlapprobability function $P(q)$ and are independent of other features of thesystem. Using solely $P(q)$ as input we can analytically predict quantitativelythe statistics of the states in a small field. In the infinite volume limit,each spin-glass sample is characterized by an infinite number of states thathave a tree-like structure. We generate the corresponding probabilitydistribution through efficient sampling using a representation based on theBolthausen-Snitmann coalescent. In this way, we can compute quantitativelyproperties in the presence of a magnetic field in the crossover region, theoverlap probability distribution in the presence of a small field and thedegree of decorrelation as the field is increased. To test our computations, wehave simulated the Bethe lattice spin glass and the 4D Edwards-Anderson model,finding in both cases excellent agreement with the universal predictions.
我们研究了自旋玻璃在外加磁场作用下的吉布斯态的混沌行为,在交叉区域,磁场强度的尺度与1/sqrt{N}$($N$为系统大小)成正比。我们的研究表明,复制对称性破坏(RSB)理论提供了混沌行为的普遍预测:它们只依赖于零磁场重叠概率函数$P(q)$,而与系统的其他特征无关。仅使用$P(q)$作为输入,我们就能定量地分析预测小场中的状态统计。在无限体积极限中,每个自旋玻璃样品都有无数个具有树状结构的状态。我们使用基于波尔索森-斯尼特曼凝聚的表示方法,通过高效采样生成相应的概率分布。通过这种方法,我们可以定量计算交叉区域存在磁场时的特性、存在小磁场时的重叠概率分布以及随着磁场增大的去相关度。为了检验我们的计算结果,我们模拟了贝特晶格自旋玻璃和 4D 爱德华-安德森模型,发现这两种情况都与普遍预测非常吻合。
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引用次数: 0
A Spin model for global flat-foldability of random origami 随机折纸全局平面可折叠性的 Spin 模型
Pub Date : 2024-03-12 DOI: arxiv-2403.07306
Chihiro Nakajima
We map the problem of determining flat-foldability of the origami diagramonto the ground-state search problem of spin glass model on random graphs. Ifthe origami diagram is locally flat-foldable around each vertex, a pre-foldeddiagram, showing the planar-positional relationship of the facet, can beobtained. For remaining combinatorial problem on layer ordering of facets canbe described as a spin model. A spin variable is assigned for thelayer-ordering of each pair of facets which have an overlap in the pre-foldeddiagram. The interactions to prohibit the intrusion of each facet into theother component of the same origami diagram are introduced among two or fourspins. The flat-foldability of the diagram is closely related to the(non-)existence of frustrated loops on the spin model with the interactions onthe random (hyper)graph.
我们把确定折纸图平面可折叠性的问题映射到随机图上自旋玻璃模型的基态搜索问题上。如果折纸图在每个顶点周围都是局部可平面折叠的,那么就可以得到一个预折叠图,它显示了面的平面位置关系。对于剩下的关于面层排序的组合问题,可以用自旋模型来描述。在预折叠图中,每一对有重叠的面的层序都有一个自旋变量。在两根或四根插针之间引入相互作用,禁止每个切面侵入同一折纸图的另一个部分。折纸图的平面可折叠性与随机(超)图上相互作用的自旋模型上(不)存在受挫环密切相关。
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引用次数: 0
Effect of Ir growth pressure on the domain wall dynamics in Ta/Pt/Co/Ir/Ta stacks Ir 生长压力对 Ta/Pt/Co/Ir/Ta 叠层畴壁动力学的影响
Pub Date : 2024-03-11 DOI: arxiv-2403.07141
P. Domenichini, J. Brock, J. Curiale, A. B. Kolton
The dynamical response of magnetic domain walls to external magnetic fieldsin ultra-thin multilayer magnetic films is determined not only by thecomposition and thickness of the layers but also by the growth conditions.Growth conditions can induce significant structural changes inside the layersand at the interfaces between them, affecting in particular the dynamics ofdomain walls, their mobility, elastic tension, and the pinning forces acting onthem. In this work, we focus specifically on the effect of Ir layer growthpressure in Ta/Pt/Co/Ir/Ta ultra-thin multilayers films. Measurements of the DCmagnetic properties, domain wall velocity and domain morphology in the creepregime for both constant and alternating field pulses, were performed for abatch of samples where the Ir layer was grown at different pressures. We findthat the saturation magnetization, the effective anisotropy constant and thedomain wall surface tension grow with increasing pressure and saturate at athreshold pressure, while the Dzyaloshinskii-Moriya field and the strength ofthe disorder remain practically unaltered over the range of pressuresconsidered.
在超薄多层磁性薄膜中,磁畴壁对外部磁场的动态响应不仅取决于层的组成和厚度,还取决于生长条件。生长条件会引起层内和层间界面的显著结构变化,尤其会影响磁畴壁的动态、其流动性、弹性张力以及作用于它们的钉力。在这项研究中,我们特别关注了 Ta/Pt/Co/Ir/Ta 超薄多层薄膜中 Ir 层生长压力的影响。在恒定和交变磁场脉冲下,我们对一批在不同压力下生长的铱层样品进行了直流电磁特性、畴壁速度和蠕变状态下的畴形貌测量。我们发现,饱和磁化、有效各向异性常数和畴壁表面张力随着压力的增加而增长,并在阈值压力下达到饱和,而 Dzyaloshinskii-Moriya 场和无序强度在所考虑的压力范围内几乎没有变化。
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引用次数: 0
Geometric Dynamics of Signal Propagation Predict Trainability of Transformers 信号传播的几何动力学预测变压器的可培训性
Pub Date : 2024-03-05 DOI: arxiv-2403.02579
Aditya Cowsik, Tamra Nebabu, Xiao-Liang Qi, Surya Ganguli
We investigate forward signal propagation and gradient back propagation indeep, randomly initialized transformers, yielding simple necessary andsufficient conditions on initialization hyperparameters that ensuretrainability of deep transformers. Our approach treats the evolution of therepresentations of $n$ tokens as they propagate through the transformer layersin terms of a discrete time dynamical system of $n$ interacting particles. Wederive simple update equations for the evolving geometry of this particlesystem, starting from a permutation symmetric simplex. Our update equationsshow that without MLP layers, this system will collapse to a line, consistentwith prior work on rank collapse in transformers. However, unlike prior work,our evolution equations can quantitatively track particle geometry in theadditional presence of nonlinear MLP layers, and it reveals an order-chaosphase transition as a function of initialization hyperparameters, like thestrength of attentional and MLP residual connections and weight variances. Inthe ordered phase the particles are attractive and collapse to a line, while inthe chaotic phase the particles are repulsive and converge to a regular$n$-simplex. We analytically derive two Lyapunov exponents: an angle exponentthat governs departures from the edge of chaos in this particle system, and agradient exponent that governs the rate of exponential growth or decay ofbackpropagated gradients. We show through experiments that, remarkably, thefinal test loss at the end of training is well predicted just by these twoexponents at the beginning of training, and that the simultaneous vanishing ofthese two exponents yields a simple necessary and sufficient condition toachieve minimal test loss.
我们在随机初始化的深度变换器中研究了前向信号传播和梯度反向传播,得出了确保深度变换器可训练性的初始化超参数的简单必要条件和充分条件。我们的方法用一个由 n 个相互作用粒子组成的离散时间动态系统来处理 n 个标记在变换器层中传播时的演化。我们从一个置换对称单纯形出发,为这个粒子系统的几何演化建立了简单的更新方程。我们的更新方程表明,如果没有 MLP 层,该系统将坍缩为一条直线,这与之前关于变压器秩坍缩的研究一致。然而,与之前的研究不同,我们的演化方程可以定量跟踪非线性 MLP 层额外存在时的粒子几何形状,它揭示了有序-混沌阶段的转变是初始化超参数的函数,如注意力和 MLP 残余连接的强度以及权重方差。在有序阶段,粒子具有吸引力并坍缩为一条线,而在混沌阶段,粒子具有排斥性并收敛为一个规则的n$复数。我们通过分析推导出两个李雅普诺夫指数:一个是控制该粒子系统偏离混沌边缘的角度指数,另一个是控制后向传播梯度指数增长或衰减速度的梯度指数。我们通过实验证明,训练结束时的最终测试损失可以通过训练开始时的这两个指数很好地预测出来,而且这两个指数的同时消失为实现最小测试损失提供了一个简单的必要条件和充分条件。
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引用次数: 0
Minimal cyclic behavior in sheared amorphous solids 剪切无定形固体中的最小循环行为
Pub Date : 2024-03-04 DOI: arxiv-2403.01679
Chloe W. Lindeman, Sidney R. Nagel
Although jammed packings of soft spheres exist in potential-energy landscapeswith a vast number of minima, when subjected to cyclic shear they may revisitthe same configurations repeatedly. Simple hysteretic spin models, in whichparticle rearrangements are represented by spin flips, capture many features ofthis periodic behavior. Yet it has been unclear to what extent individualrearrangements can be described by such binary objects. Using a particularlysensitive algorithm, we identify rearrangements in simulated jammed packings.We select pairs of rearrangements that undo one another to create periodiccyclic behavior, explore the statistics of these pairs, and show that theirinternal structure is more complex than a spin analogy would indicate. Thisoffers insight into both the collective nature of rearrangement eventsthemselves and how complex systems such as amorphous solids can reach a limitcycle with relative ease.
虽然软球的卡塞填料存在于具有大量极小值的势能景观中,但当受到周期性剪切时,它们可能会重复出现相同的构型。简单的滞后自旋模型(其中粒子的重新排列由自旋翻转表示)捕捉到了这种周期性行为的许多特征。然而,目前还不清楚这种二元对象能在多大程度上描述个体重排。我们利用一种特别灵敏的算法,在模拟的干扰填料中识别重排。我们选择了一对相互抵消以产生周期性循环行为的重排,探索了这些重排对的统计数据,并证明它们的内部结构比自旋类比所显示的更为复杂。这让我们深入了解了重排事件本身的集体性质,以及无定形固体等复杂系统如何相对容易地达到极限循环。
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引用次数: 0
Disconnectivity graphs for visualizing combinatorial optimization problems: challenges of embedding to Ising machines 用于组合优化问题可视化的断连图:嵌入伊辛机的挑战
Pub Date : 2024-03-02 DOI: arxiv-2403.01320
Dmitrii Dobrynin, Adrien Renaudineau, Mohammad Hizzani, Dmitri Strukov, Masoud Mohseni, John Paul Strachan
Physics-based Ising machines (IM) have risen to the challenge of solving hardcombinatorial optimization problems with higher speed and better energyefficiency. Generally, such dedicated systems employ local search heuristics totraverse energy landscapes in searching for optimal solutions. Extendinglandscape geometry visualization tools, disconnectivity graphs, we quantify andaddress some of the major challenges met by IMs in the field of combinatorialoptimization. Using efficient sampling methods, we visually capture landscapesof problems having diverse structure and hardness and featuring strongdegeneracies, which act as entropic barriers for IMs. Furthermore, weinvestigate energy barriers, local minima, and configuration space clusteringeffects caused by locality reduction methods when embedding combinatorialproblems to the Ising hardware. For this purpose, we sample disconnectivitygraphs of PUBO energy landscapes and their different QUBO mappings accountingfor both local minima and saddle regions. We demonstrate that QUBO energylandscape properties lead to the subpar performance of quadratic IMs andsuggest directions for their improvement.
基于物理的伊辛机(Ising machine,IM)以更高的速度和更好的能效迎接了解决硬组合优化问题的挑战。一般来说,这类专用系统采用局部搜索启发式方法遍历能量景观来寻找最优解。通过扩展地景几何可视化工具--断开图,我们量化并解决了组合优化领域中 IM 所面临的一些主要挑战。利用高效的采样方法,我们直观地捕捉到了具有不同结构和硬度的问题的景观,这些问题具有很强的退行性,成为 IM 的熵障。此外,我们还研究了将组合问题嵌入伊辛硬件时,由局部性降低方法引起的能量障碍、局部最小值和配置空间集群效应。为此,我们采样了 PUBO 能量图及其不同 QUBO 映射的断开图,并考虑了局部最小值和鞍区。我们证明了 QUBO 能量景观特性导致二次 IM 性能不佳,并提出了改进方向。
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引用次数: 0
Mobility edges in non-Hermitian models with slowly varying quasi-periodic disorders 具有缓慢变化准周期紊乱的非ermitian模型中的流动边缘
Pub Date : 2024-02-27 DOI: arxiv-2402.17266
Qiyun Tang, Yan He
We investigate the appearance of mobility edges in a one-dimensionalnon-Hermitian tight-banding model with alternating hopping constants and slowlyvarying quasi-periodic on-site potentials. Due to the presence of slowlyvarying exponent, the parity-time (PT) symmetry of this model is broken and itsspectra is complex. It is found that the spectrum of this model can be dividedinto three different types of patterns depending on the magnitude of thequasi-periodic potential. As the amplitude of the potential increases fromsmall to large, the initially well defined mobility edges become blurredgradually and then eventually disappear for large enough potential. Thisbehavior of the mobility edges is also confirmed by a detailed study of thewinding number of the complex spectra of this non-Hermitian model.
我们研究了具有交替跳变常数和慢变的准周期现场势的一维非赫米提紧带模型中流动边缘的出现。由于慢变指数的存在,该模型的奇偶性-时间(PT)对称性被打破,其频谱也变得复杂。研究发现,根据准周期电势的大小,该模型的频谱可分为三种不同的模式。当电势的振幅由小到大时,最初清晰的迁移率边缘逐渐变得模糊,当电势足够大时,迁移率边缘最终消失。对这种非赫米提模型复谱的卷绕数的详细研究也证实了流动边缘的这种行为。
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引用次数: 0
期刊
arXiv - PHYS - Disordered Systems and Neural Networks
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