We study the spectrum and transmission coefficient of plane waves propagating along square ribbons of varying widths, containing a square-shaped, PT-symmetric impurity region. We start with a zero-width ribbon (1D chain) and place a PT symmetric dimer. The spectrum is computed numerically and the instability gain is computed as a function of the gain/loss dimer strength. The transmission coefficient is obtained in closed form and examined as a function of wavevector and the gain/loss parameter. Next, we study a ribbon in a narrow ladder configuration containing a square PT impurity. As before, we compute the instability gain numerically and the transmission coefficient in closed form for the two possible input modes. Finally, we repeat the calculations for a wider ladder ribbon containing a Lieb-like impurity in a PT configuration. For all cases and transmission channels, we obtain transmission divergences in wavevector-gain/loss parameter space, whose number increases with the width of the ribbon
{"title":"Transmission across a ribbon containing a square PT impurity","authors":"Cristian Mejía-Cortés, Mario I. Molina","doi":"arxiv-2403.13217","DOIUrl":"https://doi.org/arxiv-2403.13217","url":null,"abstract":"We study the spectrum and transmission coefficient of plane waves propagating\u0000along square ribbons of varying widths, containing a square-shaped,\u0000PT-symmetric impurity region. We start with a zero-width ribbon (1D chain) and\u0000place a PT symmetric dimer. The spectrum is computed numerically and the\u0000instability gain is computed as a function of the gain/loss dimer strength. The\u0000transmission coefficient is obtained in closed form and examined as a function\u0000of wavevector and the gain/loss parameter. Next, we study a ribbon in a narrow\u0000ladder configuration containing a square PT impurity. As before, we compute the\u0000instability gain numerically and the transmission coefficient in closed form\u0000for the two possible input modes. Finally, we repeat the calculations for a\u0000wider ladder ribbon containing a Lieb-like impurity in a PT configuration. For\u0000all cases and transmission channels, we obtain transmission divergences in\u0000wavevector-gain/loss parameter space, whose number increases with the width of\u0000the ribbon","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140205765","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}
Structural glasses display at low temperature a set of anomalies in thermodynamic observables. The prominent example is the linear-in-temperature scaling of the specific heat, at odds with the Debye cubic scaling found in crystals, due to acoustic phonons. Such an excess of specific heat in amorphous solids is thought of arising from phenomenological soft excitations dubbed tunneling two-level systems (TTLS). Their nature as well as their statistical properties remain elusive from a first-principle viewpoint. In this work we investigate the canonically quantized version of the KHGPS model, a mean-field glass model of coupled anharmonic oscillators, across its phase diagram, with an emphasis on the specific heat. The thermodynamics is solved in a semiclassical expansion. We show that in the replica-symmetric region of the model, up to the marginal glass transition line where replica symmetry gets continuously broken, a disordered version of the Debye approximation holds: the specific heat is dominated by harmonic vibrational excitations inducing a power-law scaling at the transition, ruled by random matrix theory. This mechanism generalizes a previous semiclassical argument in the literature. We then study the marginal glass phase where the semiclassical expansion becomes non-perturbative due to the emergence of instantons that overcome disordered Debye behavior. Inside the glass phase, a variational solution to the instanton approach provides the prevailing excitations as TTLS, which generate a linear specific heat. This phase thus hosts a mix of TTLS and harmonic excitations generated by interactions. We finally suggest to go beyond the variational approximation through an analogy with the spin-boson model.
{"title":"Two-level systems and harmonic excitations in a mean-field anharmonic quantum glass","authors":"Thibaud Maimbourg","doi":"arxiv-2403.12740","DOIUrl":"https://doi.org/arxiv-2403.12740","url":null,"abstract":"Structural glasses display at low temperature a set of anomalies in\u0000thermodynamic observables. The prominent example is the linear-in-temperature\u0000scaling of the specific heat, at odds with the Debye cubic scaling found in\u0000crystals, due to acoustic phonons. Such an excess of specific heat in amorphous\u0000solids is thought of arising from phenomenological soft excitations dubbed\u0000tunneling two-level systems (TTLS). Their nature as well as their statistical\u0000properties remain elusive from a first-principle viewpoint. In this work we\u0000investigate the canonically quantized version of the KHGPS model, a mean-field\u0000glass model of coupled anharmonic oscillators, across its phase diagram, with\u0000an emphasis on the specific heat. The thermodynamics is solved in a\u0000semiclassical expansion. We show that in the replica-symmetric region of the\u0000model, up to the marginal glass transition line where replica symmetry gets\u0000continuously broken, a disordered version of the Debye approximation holds: the\u0000specific heat is dominated by harmonic vibrational excitations inducing a\u0000power-law scaling at the transition, ruled by random matrix theory. This\u0000mechanism generalizes a previous semiclassical argument in the literature. We\u0000then study the marginal glass phase where the semiclassical expansion becomes\u0000non-perturbative due to the emergence of instantons that overcome disordered\u0000Debye behavior. Inside the glass phase, a variational solution to the instanton\u0000approach provides the prevailing excitations as TTLS, which generate a linear\u0000specific heat. This phase thus hosts a mix of TTLS and harmonic excitations\u0000generated by interactions. We finally suggest to go beyond the variational\u0000approximation through an analogy with the spin-boson model.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168877","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}
How a closed system thermalizes, especially in the absence of global conservation laws but in the presence of disorder and interactions, is one of the central questions in non-equilibrium statistical mechanics. We explore this for a disordered, periodically driven Ising chain. Our numerical results reveal inhomogeneous thermalization leading to a distribution of thermalization timescales within a single disordered sample, which we encode via a distribution of effective local temperatures. Using this, we find an excellent collapse $textit{without}$ $textit{any}$ $textit{fitting}$ $textit{parameters}$ of the local relaxation dynamics for the entire range of disorder values in the ergodic regime when adapting the disorder-averaged diagonal entanglement entropy as internal `time' of the system. This approach evidences a remarkably uniform parametrization of the dynamical many-body evolution of local temperature within the otherwise highly heterogeneous ergodic regime, independent of the strength of the disorder.
{"title":"Inhomogeneous Floquet thermalization","authors":"Soumya Bera, Ishita Modak, Roderich Moessner","doi":"arxiv-2403.08369","DOIUrl":"https://doi.org/arxiv-2403.08369","url":null,"abstract":"How a closed system thermalizes, especially in the absence of global\u0000conservation laws but in the presence of disorder and interactions, is one of\u0000the central questions in non-equilibrium statistical mechanics. We explore this\u0000for a disordered, periodically driven Ising chain. Our numerical results reveal\u0000inhomogeneous thermalization leading to a distribution of thermalization\u0000timescales within a single disordered sample, which we encode via a\u0000distribution of effective local temperatures. Using this, we find an excellent\u0000collapse $textit{without}$ $textit{any}$ $textit{fitting}$\u0000$textit{parameters}$ of the local relaxation dynamics for the entire range of\u0000disorder values in the ergodic regime when adapting the disorder-averaged\u0000diagonal entanglement entropy as internal `time' of the system. This approach\u0000evidences a remarkably uniform parametrization of the dynamical many-body\u0000evolution of local temperature within the otherwise highly heterogeneous\u0000ergodic regime, independent of the strength of the disorder.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124786","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}
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 the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/sqrt{N}$, being $N$ the system size. We show that Replica Symmetry Breaking (RSB) theory provides universal predictions for chaotic behavior: they depend only on the zero-field overlap probability function $P(q)$ and are independent of other features of the system. Using solely $P(q)$ as input we can analytically predict quantitatively the 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 that have a tree-like structure. We generate the corresponding probability distribution through efficient sampling using a representation based on the Bolthausen-Snitmann coalescent. In this way, we can compute quantitatively properties in the presence of a magnetic field in the crossover region, the overlap probability distribution in the presence of a small field and the degree of decorrelation as the field is increased. To test our computations, we have simulated the Bethe lattice spin glass and the 4D Edwards-Anderson model, finding in both cases excellent agreement with the universal predictions.
{"title":"Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations","authors":"Miguel Aguilar-Janita, Silvio Franz, Victor Martin-Mayor, Javier Moreno-Gordo, Giorgio Parisi, Federico Ricci-Tersenghi, Juan J. Ruiz-Lorenzo","doi":"arxiv-2403.08503","DOIUrl":"https://doi.org/arxiv-2403.08503","url":null,"abstract":"We study the chaotic behavior of the Gibbs state of spin-glasses under the\u0000application of an external magnetic field, in the crossover region where the\u0000field intensity scales proportional to $1/sqrt{N}$, being $N$ the system size.\u0000We show that Replica Symmetry Breaking (RSB) theory provides universal\u0000predictions for chaotic behavior: they depend only on the zero-field overlap\u0000probability function $P(q)$ and are independent of other features of the\u0000system. Using solely $P(q)$ as input we can analytically predict quantitatively\u0000the statistics of the states in a small field. In the infinite volume limit,\u0000each spin-glass sample is characterized by an infinite number of states that\u0000have a tree-like structure. We generate the corresponding probability\u0000distribution through efficient sampling using a representation based on the\u0000Bolthausen-Snitmann coalescent. In this way, we can compute quantitatively\u0000properties in the presence of a magnetic field in the crossover region, the\u0000overlap probability distribution in the presence of a small field and the\u0000degree of decorrelation as the field is increased. To test our computations, we\u0000have simulated the Bethe lattice spin glass and the 4D Edwards-Anderson model,\u0000finding in both cases excellent agreement with the universal predictions.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124800","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}
We map the problem of determining flat-foldability of the origami diagram onto the ground-state search problem of spin glass model on random graphs. If the origami diagram is locally flat-foldable around each vertex, a pre-folded diagram, showing the planar-positional relationship of the facet, can be obtained. For remaining combinatorial problem on layer ordering of facets can be described as a spin model. A spin variable is assigned for the layer-ordering of each pair of facets which have an overlap in the pre-folded diagram. The interactions to prohibit the intrusion of each facet into the other component of the same origami diagram are introduced among two or four spins. The flat-foldability of the diagram is closely related to the (non-)existence of frustrated loops on the spin model with the interactions on the random (hyper)graph.
{"title":"A Spin model for global flat-foldability of random origami","authors":"Chihiro Nakajima","doi":"arxiv-2403.07306","DOIUrl":"https://doi.org/arxiv-2403.07306","url":null,"abstract":"We map the problem of determining flat-foldability of the origami diagram\u0000onto the ground-state search problem of spin glass model on random graphs. If\u0000the origami diagram is locally flat-foldable around each vertex, a pre-folded\u0000diagram, showing the planar-positional relationship of the facet, can be\u0000obtained. For remaining combinatorial problem on layer ordering of facets can\u0000be described as a spin model. A spin variable is assigned for the\u0000layer-ordering of each pair of facets which have an overlap in the pre-folded\u0000diagram. The interactions to prohibit the intrusion of each facet into the\u0000other component of the same origami diagram are introduced among two or four\u0000spins. The flat-foldability of the diagram is closely related to the\u0000(non-)existence of frustrated loops on the spin model with the interactions on\u0000the random (hyper)graph.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116226","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}
P. Domenichini, J. Brock, J. Curiale, A. B. Kolton
The dynamical response of magnetic domain walls to external magnetic fields in ultra-thin multilayer magnetic films is determined not only by the composition and thickness of the layers but also by the growth conditions. Growth conditions can induce significant structural changes inside the layers and at the interfaces between them, affecting in particular the dynamics of domain walls, their mobility, elastic tension, and the pinning forces acting on them. In this work, we focus specifically on the effect of Ir layer growth pressure in Ta/Pt/Co/Ir/Ta ultra-thin multilayers films. Measurements of the DC magnetic properties, domain wall velocity and domain morphology in the creep regime for both constant and alternating field pulses, were performed for a batch of samples where the Ir layer was grown at different pressures. We find that the saturation magnetization, the effective anisotropy constant and the domain wall surface tension grow with increasing pressure and saturate at a threshold pressure, while the Dzyaloshinskii-Moriya field and the strength of the disorder remain practically unaltered over the range of pressures considered.
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。
{"title":"Effect of Ir growth pressure on the domain wall dynamics in Ta/Pt/Co/Ir/Ta stacks","authors":"P. Domenichini, J. Brock, J. Curiale, A. B. Kolton","doi":"arxiv-2403.07141","DOIUrl":"https://doi.org/arxiv-2403.07141","url":null,"abstract":"The dynamical response of magnetic domain walls to external magnetic fields\u0000in ultra-thin multilayer magnetic films is determined not only by the\u0000composition and thickness of the layers but also by the growth conditions.\u0000Growth conditions can induce significant structural changes inside the layers\u0000and at the interfaces between them, affecting in particular the dynamics of\u0000domain walls, their mobility, elastic tension, and the pinning forces acting on\u0000them. In this work, we focus specifically on the effect of Ir layer growth\u0000pressure in Ta/Pt/Co/Ir/Ta ultra-thin multilayers films. Measurements of the DC\u0000magnetic properties, domain wall velocity and domain morphology in the creep\u0000regime for both constant and alternating field pulses, were performed for a\u0000batch of samples where the Ir layer was grown at different pressures. We find\u0000that the saturation magnetization, the effective anisotropy constant and the\u0000domain wall surface tension grow with increasing pressure and saturate at a\u0000threshold pressure, while the Dzyaloshinskii-Moriya field and the strength of\u0000the disorder remain practically unaltered over the range of pressures\u0000considered.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115956","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}
We investigate forward signal propagation and gradient back propagation in deep, randomly initialized transformers, yielding simple necessary and sufficient conditions on initialization hyperparameters that ensure trainability of deep transformers. Our approach treats the evolution of the representations of $n$ tokens as they propagate through the transformer layers in terms of a discrete time dynamical system of $n$ interacting particles. We derive simple update equations for the evolving geometry of this particle system, starting from a permutation symmetric simplex. Our update equations show that without MLP layers, this system will collapse to a line, consistent with prior work on rank collapse in transformers. However, unlike prior work, our evolution equations can quantitatively track particle geometry in the additional presence of nonlinear MLP layers, and it reveals an order-chaos phase transition as a function of initialization hyperparameters, like the strength of attentional and MLP residual connections and weight variances. In the ordered phase the particles are attractive and collapse to a line, while in the chaotic phase the particles are repulsive and converge to a regular $n$-simplex. We analytically derive two Lyapunov exponents: an angle exponent that governs departures from the edge of chaos in this particle system, and a gradient exponent that governs the rate of exponential growth or decay of backpropagated gradients. We show through experiments that, remarkably, the final test loss at the end of training is well predicted just by these two exponents at the beginning of training, and that the simultaneous vanishing of these two exponents yields a simple necessary and sufficient condition to achieve 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。
{"title":"Geometric Dynamics of Signal Propagation Predict Trainability of Transformers","authors":"Aditya Cowsik, Tamra Nebabu, Xiao-Liang Qi, Surya Ganguli","doi":"arxiv-2403.02579","DOIUrl":"https://doi.org/arxiv-2403.02579","url":null,"abstract":"We investigate forward signal propagation and gradient back propagation in\u0000deep, randomly initialized transformers, yielding simple necessary and\u0000sufficient conditions on initialization hyperparameters that ensure\u0000trainability of deep transformers. Our approach treats the evolution of the\u0000representations of $n$ tokens as they propagate through the transformer layers\u0000in terms of a discrete time dynamical system of $n$ interacting particles. We\u0000derive simple update equations for the evolving geometry of this particle\u0000system, starting from a permutation symmetric simplex. Our update equations\u0000show that without MLP layers, this system will collapse to a line, consistent\u0000with prior work on rank collapse in transformers. However, unlike prior work,\u0000our evolution equations can quantitatively track particle geometry in the\u0000additional presence of nonlinear MLP layers, and it reveals an order-chaos\u0000phase transition as a function of initialization hyperparameters, like the\u0000strength of attentional and MLP residual connections and weight variances. In\u0000the ordered phase the particles are attractive and collapse to a line, while in\u0000the chaotic phase the particles are repulsive and converge to a regular\u0000$n$-simplex. We analytically derive two Lyapunov exponents: an angle exponent\u0000that governs departures from the edge of chaos in this particle system, and a\u0000gradient exponent that governs the rate of exponential growth or decay of\u0000backpropagated gradients. We show through experiments that, remarkably, the\u0000final test loss at the end of training is well predicted just by these two\u0000exponents at the beginning of training, and that the simultaneous vanishing of\u0000these two exponents yields a simple necessary and sufficient condition to\u0000achieve minimal test loss.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045226","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}
Although jammed packings of soft spheres exist in potential-energy landscapes with a vast number of minima, when subjected to cyclic shear they may revisit the same configurations repeatedly. Simple hysteretic spin models, in which particle rearrangements are represented by spin flips, capture many features of this periodic behavior. Yet it has been unclear to what extent individual rearrangements can be described by such binary objects. Using a particularly sensitive algorithm, we identify rearrangements in simulated jammed packings. We select pairs of rearrangements that undo one another to create periodic cyclic behavior, explore the statistics of these pairs, and show that their internal structure is more complex than a spin analogy would indicate. This offers insight into both the collective nature of rearrangement events themselves and how complex systems such as amorphous solids can reach a limit cycle with relative ease.
{"title":"Minimal cyclic behavior in sheared amorphous solids","authors":"Chloe W. Lindeman, Sidney R. Nagel","doi":"arxiv-2403.01679","DOIUrl":"https://doi.org/arxiv-2403.01679","url":null,"abstract":"Although jammed packings of soft spheres exist in potential-energy landscapes\u0000with a vast number of minima, when subjected to cyclic shear they may revisit\u0000the same configurations repeatedly. Simple hysteretic spin models, in which\u0000particle rearrangements are represented by spin flips, capture many features of\u0000this periodic behavior. Yet it has been unclear to what extent individual\u0000rearrangements can be described by such binary objects. Using a particularly\u0000sensitive algorithm, we identify rearrangements in simulated jammed packings.\u0000We select pairs of rearrangements that undo one another to create periodic\u0000cyclic behavior, explore the statistics of these pairs, and show that their\u0000internal structure is more complex than a spin analogy would indicate. This\u0000offers insight into both the collective nature of rearrangement events\u0000themselves and how complex systems such as amorphous solids can reach a limit\u0000cycle with relative ease.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140033197","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}
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 hard combinatorial optimization problems with higher speed and better energy efficiency. Generally, such dedicated systems employ local search heuristics to traverse energy landscapes in searching for optimal solutions. Extending landscape geometry visualization tools, disconnectivity graphs, we quantify and address some of the major challenges met by IMs in the field of combinatorial optimization. Using efficient sampling methods, we visually capture landscapes of problems having diverse structure and hardness and featuring strong degeneracies, which act as entropic barriers for IMs. Furthermore, we investigate energy barriers, local minima, and configuration space clustering effects caused by locality reduction methods when embedding combinatorial problems to the Ising hardware. For this purpose, we sample disconnectivity graphs of PUBO energy landscapes and their different QUBO mappings accounting for both local minima and saddle regions. We demonstrate that QUBO energy landscape properties lead to the subpar performance of quadratic IMs and suggest 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。
{"title":"Disconnectivity graphs for visualizing combinatorial optimization problems: challenges of embedding to Ising machines","authors":"Dmitrii Dobrynin, Adrien Renaudineau, Mohammad Hizzani, Dmitri Strukov, Masoud Mohseni, John Paul Strachan","doi":"arxiv-2403.01320","DOIUrl":"https://doi.org/arxiv-2403.01320","url":null,"abstract":"Physics-based Ising machines (IM) have risen to the challenge of solving hard\u0000combinatorial optimization problems with higher speed and better energy\u0000efficiency. Generally, such dedicated systems employ local search heuristics to\u0000traverse energy landscapes in searching for optimal solutions. Extending\u0000landscape geometry visualization tools, disconnectivity graphs, we quantify and\u0000address some of the major challenges met by IMs in the field of combinatorial\u0000optimization. Using efficient sampling methods, we visually capture landscapes\u0000of problems having diverse structure and hardness and featuring strong\u0000degeneracies, which act as entropic barriers for IMs. Furthermore, we\u0000investigate energy barriers, local minima, and configuration space clustering\u0000effects caused by locality reduction methods when embedding combinatorial\u0000problems to the Ising hardware. For this purpose, we sample disconnectivity\u0000graphs of PUBO energy landscapes and their different QUBO mappings accounting\u0000for both local minima and saddle regions. We demonstrate that QUBO energy\u0000landscape properties lead to the subpar performance of quadratic IMs and\u0000suggest directions for their improvement.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140032840","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}
We investigate the appearance of mobility edges in a one-dimensional non-Hermitian tight-banding model with alternating hopping constants and slowly varying quasi-periodic on-site potentials. Due to the presence of slowly varying exponent, the parity-time (PT) symmetry of this model is broken and its spectra is complex. It is found that the spectrum of this model can be divided into three different types of patterns depending on the magnitude of the quasi-periodic potential. As the amplitude of the potential increases from small to large, the initially well defined mobility edges become blurred gradually and then eventually disappear for large enough potential. This behavior of the mobility edges is also confirmed by a detailed study of the winding number of the complex spectra of this non-Hermitian model.
{"title":"Mobility edges in non-Hermitian models with slowly varying quasi-periodic disorders","authors":"Qiyun Tang, Yan He","doi":"arxiv-2402.17266","DOIUrl":"https://doi.org/arxiv-2402.17266","url":null,"abstract":"We investigate the appearance of mobility edges in a one-dimensional\u0000non-Hermitian tight-banding model with alternating hopping constants and slowly\u0000varying quasi-periodic on-site potentials. Due to the presence of slowly\u0000varying exponent, the parity-time (PT) symmetry of this model is broken and its\u0000spectra is complex. It is found that the spectrum of this model can be divided\u0000into three different types of patterns depending on the magnitude of the\u0000quasi-periodic potential. As the amplitude of the potential increases from\u0000small to large, the initially well defined mobility edges become blurred\u0000gradually and then eventually disappear for large enough potential. This\u0000behavior of the mobility edges is also confirmed by a detailed study of the\u0000winding number of the complex spectra of this non-Hermitian model.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001785","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：