arXiv - PHYS - Chaotic Dynamics最新文献_第2页

Periodic classical trajectories and quantum scars in many-spin systems 多自旋系统中的周期经典轨迹和量子伤痕

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-30 DOI: arxiv-2409.00258

Igor Ermakov, Oleg Lychkovskiy, Boris V. Fine

{"title":"Periodic classical trajectories and quantum scars in many-spin systems","authors":"Igor Ermakov, Oleg Lychkovskiy, Boris V. Fine","doi":"arxiv-2409.00258","DOIUrl":"https://doi.org/arxiv-2409.00258","url":null,"abstract":"We numerically investigate the stability of exceptional periodic classical\u0000trajectories in rather generic chaotic many-body systems and explore a possible\u0000connection between these trajectories and exceptional nonthermal quantum\u0000eigenstates known as \"quantum many-body scars\". The systems considered are\u0000chaotic spin chains with short-range interactions, both classical and quantum.\u0000On the classical side, the chosen periodic trajectories are such that all spins\u0000instantaneously point in the same direction, which evolves as a function of\u0000time. We find that the largest Lyapunov exponents characterising the stabillity\u0000of these trajectories have surprisingly strong and nontrivial dependencies on\u0000the interaction constants and chain lengths. In particular, we identify rather\u0000long spin chains, where the above periodic trajectories are Lyapunov-stable on\u0000many-body energy shells overwhelmingly dominated by chaotic motion. We also\u0000find that instabilities around periodic trajectories in modestly large spin\u0000chains develop into a transient nearly quasiperiodic non-ergodic regime. In\u0000some cases, the lifetime of this regime is extremely long, which we interpret\u0000as a manifestation of Arnold diffusion in the vicinity of integrable dynamics.\u0000On the quantum side, we numerically investigate the dynamics of quantum states\u0000starting with all spins initially pointing in the same direction: these are the\u0000quantum counterparts of the initial conditions for the above periodic classical\u0000trajectories. Our investigation reveals the existence of quantum many-body\u0000scars for numerically accessible finite chains of spins 3/2 and higher. The\u0000dynamic thermalisation process dominated by quantum scars is shown to exhibit a\u0000slowdown in comparison with generic thermalisation at the same energy. Finally,\u0000we identify quantum signatures of the proximity to a classical separatrix of\u0000the periodic motion.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222605","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

Embedding classic chaotic maps in simple discrete-time memristor circuits 在简单离散时间忆阻器电路中嵌入经典混沌图

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-29 DOI: arxiv-2408.16352

Mauro Di Marco, Mauro Forti, Giacomo Innocenti, Luca Pancioni, Alberto Tesi

{"title":"Embedding classic chaotic maps in simple discrete-time memristor circuits","authors":"Mauro Di Marco, Mauro Forti, Giacomo Innocenti, Luca Pancioni, Alberto Tesi","doi":"arxiv-2408.16352","DOIUrl":"https://doi.org/arxiv-2408.16352","url":null,"abstract":"In the last few years the literature has witnessed a remarkable surge of\u0000interest for maps implemented by discrete-time (DT) memristor circuits. This\u0000paper investigates on the reasons underlying this type of complex behavior. To\u0000this end, the papers considers the map implemented by the simplest memristor\u0000circuit given by a capacitor and an ideal flux-controlled memristor or an\u0000inductor and an ideal charge-controlled memristor. In particular, the\u0000manuscript uses the DT flux-charge analysis method (FCAM) introduced in a\u0000recent paper to ensure that the first integrals and foliation in invariant\u0000manifolds of continuous-time (CT) memristor circuits are preserved exactly in\u0000the discretization for any step size. DT-FCAM yields a two-dimensional map in\u0000the voltage-current domain (VCD) and a manifold-dependent one-dimensional map\u0000in the flux-charge domain (FCD), i.e., a one-dimensional map on each invariant\u0000manifold. One main result is that, for suitable choices of the circuit\u0000parameters and memristor nonlinearities, both DT circuits can exactly embed two\u0000classic chaotic maps, i.e., the logistic map and the tent map. Moreover, due to\u0000the property of extreme multistability, the DT circuits can simultaneously\u0000embed in the manifolds all the dynamics displayed by varying one parameter in\u0000the logistic and tent map. The paper then considers a DT memristor\u0000Murali-Lakshmanan-Chua circuit and its dual. Via DT-FCAM these circuits\u0000implement a three-dimensional map in the VCD and a two-dimensional map on each\u0000invariant manifold in the FCD. It is shown that both circuits can\u0000simultaneously embed in the manifolds all the dynamics displayed by two other\u0000classic chaotic maps, i.e., the Henon map and the Lozi map, when varying one\u0000parameter in such maps. In essence, these results provide an explanation of why\u0000it is not surprising to observe complex dynamics even in simple DT memristor\u0000circuits.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222570","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

Characterization of dynamical systems with scanty data using Persistent Homology and Machine Learning 利用持久同源性和机器学习表征数据稀少的动力系统

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-28 DOI: arxiv-2408.15834

Rishab Antosh, Sanjit Das, N. Nirmal Thyagu

{"title":"Characterization of dynamical systems with scanty data using Persistent Homology and Machine Learning","authors":"Rishab Antosh, Sanjit Das, N. Nirmal Thyagu","doi":"arxiv-2408.15834","DOIUrl":"https://doi.org/arxiv-2408.15834","url":null,"abstract":"Determination of the nature of the dynamical state of a system as a function\u0000of its parameters is an important problem in the study of dynamical systems.\u0000This problem becomes harder in experimental systems where the obtained data is\u0000inadequate (low-res) or has missing values. Recent developments in the field of\u0000topological data analysis have given a powerful methodology, viz. persistent\u0000homology, that is particularly suited for the study of dynamical systems.\u0000Earlier studies have mapped the dynamical features with the topological\u0000features of some systems. However, these mappings between the dynamical\u0000features and the topological features are notional and inadequate for accurate\u0000classification on two counts. First, the methodologies employed by the earlier\u0000studies heavily relied on human validation and intervention. Second, this\u0000mapping done on the chaotic dynamical regime makes little sense because\u0000essentially the topological summaries in this regime are too noisy to extract\u0000meaningful features from it. In this paper, we employ Machine Learning (ML)\u0000assisted methodology to minimize the human intervention and validation of\u0000extracting the topological summaries from the dynamical states of systems.\u0000Further, we employ a metric that counts in the noisy topological summaries,\u0000which are normally discarded, to characterize the state of the dynamical system\u0000as periodic or chaotic. This is surprisingly different from the conventional\u0000methodologies wherein only the persisting (long-lived) topological features are\u0000taken into consideration while the noisy (short-lived) topological features are\u0000neglected. We have demonstrated our ML-assisted method on well-known systems\u0000such as the Lorentz, Duffing, and Jerk systems. And we expect that our\u0000methodology will be of utility in characterizing other dynamical systems\u0000including experimental systems that are constrained with limited data.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"436 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222572","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

Machine Learning of Nonlinear Dynamical Systems with Control Parameters Using Feedforward Neural Networks 利用前馈神经网络对带有控制参数的非线性动态系统进行机器学习

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-28 DOI: arxiv-2409.07468

Hidetsugu Sakaguchi

引用次数: 0

Route to chaos and resonant triads interaction in a truncated Rotating Nonlinear shallow-water model 截断旋转非线性浅水模型中的混沌与共振三元相互作用之路

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-26 DOI: arxiv-2408.14495

Francesco Carbone, Denys Dutykh

{"title":"Route to chaos and resonant triads interaction in a truncated Rotating Nonlinear shallow-water model","authors":"Francesco Carbone, Denys Dutykh","doi":"arxiv-2408.14495","DOIUrl":"https://doi.org/arxiv-2408.14495","url":null,"abstract":"The route to chaos and phase dynamics in a rotating shallow-water model were\u0000rigorously examined using a five-mode Galerkin truncated system with complex\u0000variables. This system is valuable for investigating how large/meso-scales\u0000destabilize and evolve into chaos. Two distinct transitions into chaotic\u0000behaviour were identified as energy levels increased. The initial transition\u0000occurs through bifurcations following the Feigenbaum sequence. The subsequent\u0000transition, at higher energy levels, shows a shift from quasi-periodic states\u0000to chaotic regimes. The first chaotic state is mainly due to inertial forces\u0000governing nonlinear interactions. The second chaotic state arises from the\u0000increased significance of free surface elevation in the dynamics. A novel\u0000reformulation using phase and amplitude representations for each truncated\u0000variable revealed that phase components exhibit a temporal piece-wise locking\u0000behaviour, maintaining a constant value for a prolonged interval before an\u0000abrupt transition of $pmpi$, while amplitudes remain chaotic. It was observed\u0000that phase stability duration decreases with increased energy, leading to chaos\u0000in phase components at high energy levels. This is attributed to the nonlinear\u0000term in the equations, where phase components are introduced through linear\u0000combinations of triads with different modes. When locking durations vary across\u0000modes, the dynamics result in a stochastic interplay of multiple $pi$ phase\u0000shifts, creating a stochastic dynamic within the coupled phase triads,\u0000observable even at minimal energy injections.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222573","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

Mapping Chaos: Bifurcation Patterns and Shrimp Structures in the Ikeda Map 混沌地图：池田地图中的分岔模式和虾米结构

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-21 DOI: arxiv-2408.11254

Diego F. M. Oliveira

引用次数: 0

Shearless bifurcations for two isochronous resonant perturbations 两个等时共振扰动的无剪切分岔

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-20 DOI: arxiv-2408.10930

Bruno B. Leal, Matheus J. Lazarotto, Michele Mugnaine, Alfredo M. Ozorio de Almeida, Ricardo L. Viana, Iberê L. Caldas

引用次数: 0

A dynamical systems perspective on the celestial mechanical contribution to the emergence of life 从动力系统角度看天体机械对生命出现的贡献

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-20 DOI: arxiv-2408.10544

Fan Zhang

{"title":"A dynamical systems perspective on the celestial mechanical contribution to the emergence of life","authors":"Fan Zhang","doi":"arxiv-2408.10544","DOIUrl":"https://doi.org/arxiv-2408.10544","url":null,"abstract":"Biological activities are often seen entrained onto the day-night and other\u0000celestial mechanical cycles (e.g., seasonal and lunar), but studies on the\u0000origin of life have largely not accounted for such periodic external\u0000environmental variations. We argue that this may be an important omission,\u0000because the signature replication behaviour of life represents temporal memory\u0000in the dynamics of ecosystems, that signifies the absence of mixing properties\u0000(i.e., the dynamics are not fully chaotic), and entrainment onto regular,\u0000periodic external perturbative influences has been proven capable of\u0000suppressing chaos, and thus may bring otherwise unstable chemical reaction sets\u0000into viability, as precursors to abiogenesis. As well, external perturbations\u0000may be necessary to prevent an open dissipative (bio)chemical system from\u0000collapsing into the opposite extreme -- the point attractor of thermal\u0000equilibrium. In short, life may precariously rest on the edge of chaos, and\u0000open-loop periodic perturbation rooted in celestial mechanics (and should be\u0000simulated in laboratory experiments in origin-of-life studies) may help with\u0000the balancing. Such considerations, if pertinent, would also be consequential\u0000to exobiology, e.g., in regard to tidal-locking properties of potential host\u0000worlds.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222575","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

Chaotic uncertainty and statistical inference for natural chaotic systems: Choosing predictors for multiple season ahead prediction of precipitation, Extended and Annotated 自然混沌系统的混沌不确定性和统计推断：为多季降水超前预测选择预测因子》，扩展和注释版

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-16 DOI: arxiv-2409.00023

Michael LuValle

引用次数: 0

Identifying Patterns Using Cross-Correlation Random Matrices Derived from Deterministic and Stochastic Differential Equations 利用从确定性和随机微分方程得出的交叉相关随机矩阵识别模式

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-08-15 DOI: arxiv-2408.08237

Roberto da Silva, Sandra D. Prado

引用次数: 0