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Non-Hermitian butterfly spectra in a family of quasiperiodic lattices 准周期晶格族中的非ermitian 蝴蝶谱
Pub Date : 2024-04-17 DOI: arxiv-2404.11020
Li Wang, Zhenbo Wang, Shu Chen
We propose a family of exactly solvable quasiperiodic lattice models withanalytical complex mobility edges, which can incorporate mosaic modulations asa straightforward generalization. By sweeping a potential tuning parameter$delta$, we demonstrate a kind of interesting butterfly-like spectra incomplex energy plane, which depicts energy-dependent extended-localizedtransitions sharing a common exact non-Hermitian mobility edge. ApplyingAvila's global theory, we are able to analytically calculate the Lyapunovexponents and determine the mobility edges exactly. For the minimal modelwithout mosaic modulation, a compactly analytic formula for the complexmobility edges is obtained, which, together with analytical estimation of therange of complex energy spectrum, gives the true mobility edge. Thenon-Hermitian mobility edge in complex energy plane is further verified bynumerical calculations of fractal dimension and spatial distribution of wavefunctions. Tuning parameters of non-Hermitian potentials, we also investigatethe variations of the non-Hermitian mobility edges and the correspondingbutterfly spectra, which exhibit richness of spectrum structures.
我们提出了一系列可精确求解的准周期晶格模型,这些模型具有分析性复数迁移率边沿,可以直接概括为镶嵌调制。通过扫频势能调谐参数$delta$,我们展示了一种有趣的非复数能面蝴蝶谱,它描述了依赖能量的扩展局部转变,共享一个共同的精确非ermitian 移动边。应用阿维拉的全局理论,我们能够分析计算 Lyapunovexponents 并精确确定流动边缘。对于无镶嵌调制的最小模型,我们得到了复能流动边的紧凑解析公式,再加上对复能谱范围的解析估计,就得到了真正的流动边。然后,通过分形维度和波函数空间分布的数值计算,进一步验证了复能面上的非ermitian 移动性边缘。通过调整非ermitian 势的参数,我们还研究了非ermitian 移动性边缘的变化以及相应的蝶形谱,这些变化展示了丰富的谱结构。
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引用次数: 0
Heterogeneous mean-field analysis of the generalized Lotka-Volterra model on a network 网络上广义洛特卡-伏特拉模型的异质均场分析
Pub Date : 2024-04-17 DOI: arxiv-2404.11164
Fabián Aguirre-López
We study the dynamics of the generalized Lotka-Volterra model with a networkstructure. Performing a high connectivity expansion for graphs, we write down amean-field dynamical theory that incorporates degree heterogeneity. This allowsus to describe the fixed points of the model in terms of a few simple orderparameters. We extend the analysis even for diverging abundances, using amapping to the replicator model. With this we present a unified approach forboth cooperative and competitive systems that display complementary behaviors.In particular we show the central role of an order parameter called thecritical degree, $g_c$. In the competitive regime $g_c$ serves to distinguishhigh degree nodes that are more likely to go extinct, while in the cooperativeregime it has the reverse role, it will determine the low degree nodes thattend to go relatively extinct.
我们研究了具有网络结构的广义洛特卡-伏特拉模型的动力学。通过对图进行高连接性扩展,我们写出了包含度异质性的均场动力学理论。这使得我们可以用几个简单的阶参数来描述模型的定点。我们利用复制器模型的映射,扩展了对发散丰度的分析。因此,我们提出了一种同时适用于合作和竞争系统的统一方法,这两种系统显示出互补的行为。在竞争系统中,g_c$ 的作用是区分更有可能消亡的高程度节点,而在合作系统中,它的作用正好相反,它将决定倾向于相对消亡的低程度节点。
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引用次数: 0
Haldane graphene billiards versus relativistic neutrino billiards 霍尔丹石墨烯台球与相对论中微子台球
Pub Date : 2024-04-11 DOI: arxiv-2404.07679
Dung Xuan Nguyen, Barbara Dietz
We study fluctuation properties in the energy spectra of finite-sizehoneycomb lattices, graphene billiards, subject to the Haldane-model onsitepotential and next-nearest neighbor interaction at critical points, referred toas Haldane graphene billiards in the following. The billiards had the shapes ofa rectangular billiard with integrable dynamics, one with chaotic dynamics, andone whose shape has, in addition, threefold rotational symmetry. It had beenshown that the spectral properties of the graphene billiards coincide withthose of the nonrelativistic quantum billiard with the corresponding shape,both at the band edges and in the region of low energy excitations around theDirac points at zero energy. There, the dispersion relation is linear and,accordingly, the spectrum is described by the same relativistic Dirac equationfor massless half-spin particles as relativistic neutrino billiards, whosespectral properties agree with those of nonrelativistic quantum billiards withviolated time-reversal invariance. Deviations from the expected behavior areattributed to differing boundary conditions and backscattering at the boundary,which leads to a mixing of valley states corresponding to the two Dirac points,that are mapped into each other through time reversal. We employ a Haldanemodel to introduce a gap at one of the two Dirac points so that backscatteringis suppressed in the energy region of the gap and demonstrate that there thecorrelations in the spectra comply with those of the neutrino billiard of thecorresponding shape.
我们研究了有限尺寸的蜂窝状晶格--石墨烯台球--的能谱波动特性,其临界点受霍尔丹模型的原位势能和近邻相互作用的影响,下文称之为霍尔丹石墨烯台球。这些石墨烯台球的形状包括具有可积分动力学的矩形台球、具有混沌动力学的矩形台球和具有三重旋转对称性的矩形台球。研究表明,石墨烯台球的光谱特性与具有相应形状的非相对论量子台球的光谱特性相吻合,无论是在能带边缘还是在零能量的迪拉克点附近的低能激发区域。在那里,色散关系是线性的,因此,频谱是用与相对论中微子台球相同的相对论狄拉克方程来描述无质量半自旋粒子的,其频谱特性与违反了时间反转不变性的非相对论量子台球的频谱特性一致。与预期行为的偏差归因于不同的边界条件和边界的反向散射,这导致了对应于两个狄拉克点的谷态的混合,而这两个狄拉克点又通过时间反转相互映射。我们采用哈当模型在两个狄拉克点中的一个点上引入间隙,使反向散射在间隙的能量区域被抑制,并证明在那里光谱中的相关性符合相应形状的中微子台球的相关性。
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引用次数: 0
A random matrix model for the density of states of jammed soft spheres with applied stress 具有外加应力的卡塞软球状态密度的随机矩阵模型
Pub Date : 2024-04-10 DOI: arxiv-2404.07064
Mario Pernici
We investigate the addition of applied stress to a random block matrix modelintroduced by Parisi to study the Hessian matrix of soft spheres near thejamming point. In the infinite dimensional limit the applied stress translatesthe spectral distribution to the left, leading to a stability constraint. Withnegative stress, as in the case of a random network of stretched elasticsprings, the spectral distribution is translated to the right, and the densityof states has a peak before the plateau.
我们研究了在帕里西引入的随机块矩阵模型中加入外加应力的问题,该模型用于研究干扰点附近软球的 Hessian 矩阵。在无限维极限中,外加应力会将频谱分布向左平移,从而导致稳定性约束。负应力时,如拉伸弹簧的随机网络,频谱分布向右平移,状态密度在高原之前有一个峰值。
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引用次数: 0
Unsupervised machine learning for supercooled liquids 针对过冷液体的无监督机器学习
Pub Date : 2024-04-06 DOI: arxiv-2404.04473
Yunrui Qiu, Inhyuk Jang, Xuhui Huang, Arun Yethiraj
Unraveling dynamic heterogeneity in supercooled liquids from structuralinformation is one of the grand challenges of physics. In this work, weintroduce an unsupervised machine learning approach based on a time-laggedautoencoder (TAE) to elucidate the effect of structural features on thelong-term dynamics of supercooled liquids. The TAE uses an autoencoder toreconstruct features at time $t + Delta t$ from input features at time $t$ forindividual particles, and the resulting latent space variables are consideredas order parameters. In the Kob-Andersen system, with a $Delta t$ about athousand times smaller than the relaxation time, the TAE order parameterexhibits a remarkable correlation with the long-time propensity. We find thatshort-range radial features correlate with the short-time dynamics, andmedium-range radial features correlate with the long-time dynamics. This showsthat fluctuations of medium-range structural features contain sufficientinformation about the long-time dynamic heterogeneity, consistent with sometheoretical predictions.
从结构信息中揭示过冷液体的动态异质性是物理学的重大挑战之一。在这项工作中,我们引入了一种基于时滞自动编码器(TAE)的无监督机器学习方法,以阐明结构特征对过冷液体长期动力学的影响。TAE 使用自动编码器从单个粒子在时间 $t$ 的输入特征重建时间 $t + Delta t$ 的特征,并将由此产生的潜在空间变量视为阶次参数。在 Kob-Andersen 系统中,当 $Delta t$ 小于弛豫时间约几千倍时,TAE 的阶次参数与长时倾向有显著的相关性。我们发现短程径向特征与短时动力学相关,而中程径向特征与长时动力学相关。这表明中程结构特征的波动包含了关于长时动态异质性的足够信息,这与某些理论预测是一致的。
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引用次数: 0
Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics 重访查克-科丁顿模型的实空间重正化方法:改进的统计数据
Pub Date : 2024-03-31 DOI: arxiv-2404.00660
Syl Shaw, Rudolf A. Römer
The real-space renormalisation group method can be applied to theChalker-Coddington model of the quantum Hall transition to provide a convenientnumerical estimation of the localisation critical exponent, $nu$. Previoussuch studies found $nusim 2.39$ which falls considerably short of the currentbest estimates by transfer matrix ($nuapprox 2.593$) andexact-diagonalisation studies ($nu=2.58(3)$). By increasing the amount of data$500$ fold we can now measure closer to the critical point and find an improvedestimate $nuapprox 2.51$. This deviates only $sim 3%$ from the previous twovalues and is already better than the $sim 7%$ accuracy of the classicalsmall-cell renormalisation approach from which our method is adapted. We alsostudy a previously proposed mixing of the Chalker-Coddington model with aclassical scattering model which is meant to provide a route to understandingwhy experimental estimates give a lower $nusim 2.3$. Upon implementing thismixing into our RG unit, we find only further increases to the value of $nu$.
实空间重正化群方法可以应用于量子霍尔转换的查克-科丁顿模型,从而对局域化临界指数($nu$)进行方便的数值估计。之前的研究发现$nusim 2.39$大大低于目前通过转移矩阵($nuapprox 2.593$)和精确对角研究($nu=2.58(3)$)得出的最佳估计值。通过增加500倍的数据量,我们现在可以测量到更接近临界点的数据,并找到一个改进的估计值 $nuapprox 2.51$。这与之前的两个数值仅相差 $sim 3%$ ,已经优于经典小室重正化方法的精度 $sim 7%$ ,而我们的方法正是从经典小室重正化方法改编而来的。我们还研究了之前提出的将查克-科丁顿模型与经典散射模型混合的方法,其目的是为理解为什么实验估计值会低于2.3美元提供一条途径。在我们的RG单元中实施这种混合后,我们发现$nu$的值只会进一步增加。
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引用次数: 0
High entropy metallic glasses, what does it mean? 高熵金属眼镜,它意味着什么?
Pub Date : 2024-03-29 DOI: arxiv-2403.20115
G. V. Afonin, J. C. Qiao, A. S. Makarov, R. A. Konchakov, E. V. Goncharova, N. P. Kobelev, V. A. Khonik
We performed calorimetric measurements on 30 bulk metallic glasses differingwith their mixing entropies DSmix. On this basis, the excess entropies DS andexcess enthalpies DH of glasses with respect to their maternal crystallinestates are calculated. It is found that the excess entropy DS on the averagedecreases with increasing mixing entropy DSmix. This means that so-called"high-entropymetallic glasses" (i.e. the glasses having high DSmix) actuallyconstitute glasses with low excess entropy DS. We predict that such glassesshould have reduced relaxation ability. We also found that the excess enthalpyDH of glass linearly increases with its excess entropy DS, in line with ageneral thermodynamic estimate.
我们对 30 种不同混合熵 DSmix 的块状金属玻璃进行了量热测量。在此基础上,计算了玻璃相对于母晶状态的过量熵 DS 和过量焓 DH。结果发现,平均过剩熵 DS 随混合熵 DSmix 的增加而减小。这意味着所谓的 "高熵金属玻璃"(即具有高混合熵 DSmix 的玻璃)实际上是由低过剩熵 DS 的玻璃构成的。我们预测这类玻璃的弛豫能力会降低。我们还发现,玻璃的过剩焓DH随过剩熵DS的增加而线性增加,这与一般的热力学估计一致。
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引用次数: 0
Arbitrage equilibrium and the emergence of universal microstructure in deep neural networks 套利均衡与深度神经网络中普遍微观结构的出现
Pub Date : 2024-03-29 DOI: arxiv-2405.10955
Venkat Venkatasubramanian, N Sanjeevrajan, Manasi Khandekar, Abhishek Sivaram, Collin Szczepanski
Despite the stunning progress recently in large-scale deep neural networkapplications, our understanding of their microstructure, 'energy' functions,and optimal design remains incomplete. Here, we present a new game-theoreticframework, called statistical teleodynamics, that reveals important insightsinto these key properties. The optimally robust design of such networksinherently involves computational benefit-cost trade-offs that are notadequately captured by physics-inspired models. These trade-offs occur asneurons and connections compete to increase their effective utilities underresource constraints during training. In a fully trained network, this resultsin a state of arbitrage equilibrium, where all neurons in a given layer havethe same effective utility, and all connections to a given layer have the sameeffective utility. The equilibrium is characterized by the emergence of twolognormal distributions of connection weights and neuronal output as theuniversal microstructure of large deep neural networks. We call such a networkthe Jaynes Machine. Our theoretical predictions are shown to be supported byempirical data from seven large-scale deep neural networks. We also show thatthe Hopfield network and the Boltzmann Machine are the same special case of theJaynes Machine.
尽管最近在大规模深度神经网络应用方面取得了令人惊叹的进展,但我们对其微观结构、"能量 "函数和优化设计的理解仍然不全面。在这里,我们提出了一种新的博弈论框架,称为统计远程动力学,揭示了对这些关键特性的重要见解。此类网络的最佳鲁棒性设计本质上涉及计算效益与成本的权衡,而物理启发模型并不能充分捕捉到这一点。在训练过程中,神经元和连接会在资源限制下竞相提高其有效效用,从而产生这些权衡。在一个经过充分训练的网络中,这会导致一种套利平衡状态,即给定层中的所有神经元具有相同的有效效用,给定层的所有连接具有相同的有效效用。这种平衡的特点是出现了连接权重和神经元输出的双正态分布,这是大型深度神经网络的普遍微观结构。我们把这样的网络称为杰恩斯机器。七个大型深度神经网络的经验数据证明了我们的理论预测。我们还证明,Hopfield 网络和玻尔兹曼机是杰恩斯机的同一特例。
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引用次数: 0
Random Apollonian networks with tailored clustering coefficient 具有定制聚类系数的随机阿波罗网络
Pub Date : 2024-03-27 DOI: arxiv-2403.18615
Eduardo M. K. Souza, Guilherme M. A. Almeida
We introduce a family of complex networks that interpolates between theApollonian network and its binary version, recently introduced in [Phys. Rev. Etextbf{107}, 024305 (2023)], via random removal of nodes. The dilution processallows the clustering coefficient to vary from $C=0.828$ to $C=0$ whilemaintaining the behavior of average path length and other relevant quantitiesas in the deterministic Apollonian network. Robustness against the randomdeletion of nodes is also reported on spectral quantities such as theground-state localization degree and its energy gap to the first excited state.The loss of the $2pi / 3$ rotation symmetry as a tree-like network emerges isinvestigated in the light of the hub wavefunction amplitude. Our findingsexpose the interplay between the small-world property and other distinctivetraits exhibited by Apollonian networks, as well as their resilience againstrandom attacks.
我们介绍了一种复杂网络族,它通过随机删除节点,在阿波罗网络和最近在[Phys. Rev. Etextbf{107}, 024305 (2023)]中介绍的其二进制版本之间进行插值。稀释过程允许聚类系数从$C=0.828$变化到$C=0$,同时保持了确定性阿波罗网络中的平均路径长度和其他相关量的行为。我们还报告了节点随机删除对光谱量的稳健性,如基态定位度及其到第一激发态的能隙。我们的发现揭示了阿波罗网络的小世界特性和其他独特特征之间的相互作用,以及它们对随机攻击的抵御能力。
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引用次数: 0
Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model 非互惠长程奥布里-安德烈-哈珀模型中出现的随强度变化的无标度流动边缘
Pub Date : 2024-03-25 DOI: arxiv-2403.16739
Gui-Juan Liu, Jia-Ming Zhang, Shan-Zhong Li, Zhi Li
We investigate the properties of mobility edge in an Aubry-Andr'e-Harpermodel with non-reciprocal long-range hopping. The results reveal that there canbe a new type of mobility edge featuring both strength-dependent and scale-freeproperties. By calculating the fractal dimension, we find that the positions ofmobility edges are robust to the strength of non-reciprocal long-range hopping.Furthermore, through scale analysis of the observables such as fractaldimension, eigenenergy and eigenstate, etc., we prove that four differentspecific mobility edges can be observed in the system. This paper extends thefamily tree of mobility edges and hopefully it will shed more light on therelated theory and experiment.
我们研究了具有非互惠长程跳变的奥布里-安德烈-哈珀模型中的流动边缘特性。结果表明,可能存在一种新型的流动边缘,它同时具有强度依赖性和无标度特性。此外,通过对分形维度、特征能和特征态等观测指标的尺度分析,我们证明了在系统中可以观察到四种不同的流动边缘。本文扩展了流动边缘的家族树,希望能为相关理论和实验提供更多启示。
{"title":"Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model","authors":"Gui-Juan Liu, Jia-Ming Zhang, Shan-Zhong Li, Zhi Li","doi":"arxiv-2403.16739","DOIUrl":"https://doi.org/arxiv-2403.16739","url":null,"abstract":"We investigate the properties of mobility edge in an Aubry-Andr'e-Harper\u0000model with non-reciprocal long-range hopping. The results reveal that there can\u0000be a new type of mobility edge featuring both strength-dependent and scale-free\u0000properties. By calculating the fractal dimension, we find that the positions of\u0000mobility edges are robust to the strength of non-reciprocal long-range hopping.\u0000Furthermore, through scale analysis of the observables such as fractal\u0000dimension, eigenenergy and eigenstate, etc., we prove that four different\u0000specific mobility edges can be observed in the system. This paper extends the\u0000family tree of mobility edges and hopefully it will shed more light on the\u0000related theory and experiment.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
期刊
arXiv - PHYS - Disordered Systems and Neural Networks
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