M. Wanic, C. Jasiukiewicz, Z. Toklikishvili, V. Jandieri, M. Trybus, E. Jartych, S. K. Mishra, L. Chotorlishvili
Optomagnonics is a new field of research in condensed matter physics and quantum optics focused on strong magnon-photon interactions. Particular interest concerns realistic, experimentally feasible materials and prototype cheap elements for futuristic nanodevices implemented in the processing or storing of quantum information. Quantifying the entanglement between two continuous bosonic modes, such as magnons and photons, is not trivial. The state-of-the-art for today is the logarithmic negativity, calculated through the quantum Langevin equations subjected to thermal noise. However, due to its complexity, this method requires further approximation. In the present work, we propose a new procedure that avoids the linearization of dynamics. Prior analyzing the quantum entanglement, we explore the nonlinear semiclassical dynamics in detail and precisely define the phase space. The typical nonlinear dynamical system holds bifurcation points and fixed points of different characters in its phase space. Our main finding is that entanglement is not defined in the Saddle Point region. On the other hand, the maximum of the entanglement corresponds to the region near the border between the Stable node and Stable spiral regions. In numerical calculations, we considered a particular system: optomagnonic crystal based on the yttrium iron garnet (YIG) slab with the periodic air holes drilled in the slab. In our case, Magnon-photon interaction occurs due to the magneto-electric effect in YIG. We provide explicit derivation of the coupling term. Besides, we calculate photon modes for a particular geometry of the optomagnonic crystal. We analyzed the amplitude-frequency characteristics of the optomagnonic crystal and showed that due to the instability region, one could efficiently switch the mean magnon numbers in the system and control entanglement in the system.
{"title":"Entanglement properties of optomagnonic crystal from nonlinear perspective","authors":"M. Wanic, C. Jasiukiewicz, Z. Toklikishvili, V. Jandieri, M. Trybus, E. Jartych, S. K. Mishra, L. Chotorlishvili","doi":"arxiv-2406.09074","DOIUrl":"https://doi.org/arxiv-2406.09074","url":null,"abstract":"Optomagnonics is a new field of research in condensed matter physics and\u0000quantum optics focused on strong magnon-photon interactions. Particular\u0000interest concerns realistic, experimentally feasible materials and prototype\u0000cheap elements for futuristic nanodevices implemented in the processing or\u0000storing of quantum information. Quantifying the entanglement between two\u0000continuous bosonic modes, such as magnons and photons, is not trivial. The\u0000state-of-the-art for today is the logarithmic negativity, calculated through\u0000the quantum Langevin equations subjected to thermal noise. However, due to its\u0000complexity, this method requires further approximation. In the present work, we\u0000propose a new procedure that avoids the linearization of dynamics. Prior\u0000analyzing the quantum entanglement, we explore the nonlinear semiclassical\u0000dynamics in detail and precisely define the phase space. The typical nonlinear\u0000dynamical system holds bifurcation points and fixed points of different\u0000characters in its phase space. Our main finding is that entanglement is not\u0000defined in the Saddle Point region. On the other hand, the maximum of the\u0000entanglement corresponds to the region near the border between the Stable node\u0000and Stable spiral regions. In numerical calculations, we considered a\u0000particular system: optomagnonic crystal based on the yttrium iron garnet (YIG)\u0000slab with the periodic air holes drilled in the slab. In our case,\u0000Magnon-photon interaction occurs due to the magneto-electric effect in YIG. We\u0000provide explicit derivation of the coupling term. Besides, we calculate photon\u0000modes for a particular geometry of the optomagnonic crystal. We analyzed the\u0000amplitude-frequency characteristics of the optomagnonic crystal and showed that\u0000due to the instability region, one could efficiently switch the mean magnon\u0000numbers in the system and control entanglement in the system.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515166","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}
Distribution of colors and patterns in images is observed through cascades that adjust spatial resolution and dynamics. Cascades of colors reveal the emergent universal property that Fully Colored Images (FCIs) of natural scenes adhere to the debated continuous linear log-scale law (slope $-2.00 pm 0.01$) (L1). Cascades of discrete $2 times 2$ patterns are derived from pixel squares reductions onto the seven unlabeled rotation-free textures (0000, 0001, 0011, 0012, 0101, 0102, 0123). They exhibit an unparalleled universal entropy maximum of $1.74 pm 0.013$ at some dynamics regardless of spatial scale (L2). Patterns also adhere to the Integral Fluctuation Theorem ($1.00 pm 0.01$) (L3), pivotal in studies of chaotic systems. Images with fewer colors exhibit quadratic shift and bias from L1 and L3 but adhere to L2. Randomized Hilbert fractals FCIs better match the laws than basic-to-AI-based simulations. Those results are of interest in Neural Networks, out of equilibrium physics and spectral imagery.
{"title":"Universal Scale Laws for Colors and Patterns in Imagery","authors":"Rémi Michel, Mohamed Tamaazousti","doi":"arxiv-2406.08149","DOIUrl":"https://doi.org/arxiv-2406.08149","url":null,"abstract":"Distribution of colors and patterns in images is observed through cascades\u0000that adjust spatial resolution and dynamics. Cascades of colors reveal the\u0000emergent universal property that Fully Colored Images (FCIs) of natural scenes\u0000adhere to the debated continuous linear log-scale law (slope $-2.00 pm 0.01$)\u0000(L1). Cascades of discrete $2 times 2$ patterns are derived from pixel squares\u0000reductions onto the seven unlabeled rotation-free textures (0000, 0001, 0011,\u00000012, 0101, 0102, 0123). They exhibit an unparalleled universal entropy maximum\u0000of $1.74 pm 0.013$ at some dynamics regardless of spatial scale (L2). Patterns\u0000also adhere to the Integral Fluctuation Theorem ($1.00 pm 0.01$) (L3), pivotal\u0000in studies of chaotic systems. Images with fewer colors exhibit quadratic shift\u0000and bias from L1 and L3 but adhere to L2. Randomized Hilbert fractals FCIs\u0000better match the laws than basic-to-AI-based simulations. Those results are of\u0000interest in Neural Networks, out of equilibrium physics and spectral imagery.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515167","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}
Matheus Rolim Sales, Daniel Borin, Leonardo Costa de Souza, José Danilo Szezech Jr., Ricardo Luiz Viana, Iberê Luiz Caldas, Edson Denis Leonel
We investigate the transport of particles in the chaotic component of phase space for a two-dimensional, area-preserving nontwist map. The survival probability for particles within the chaotic sea is described by an exponential decay for regions in phase space predominantly chaotic and it is scaling invariant in this case. Alternatively, when considering mixed chaotic and regular regions, there is a deviation from the exponential decay, characterized by a power law tail for long times, a signature of the stickiness effect. Furthermore, due to the asymmetry of the chaotic component of phase space with respect to the line $I = 0$, there is an unbalanced stickiness which generates a ratchet current in phase space. Finally, we perform a phenomenological description of the diffusion of chaotic particles by identifying three scaling hypotheses, and obtaining the critical exponents via extensive numerical simulations.
{"title":"Ratchet current and scaling properties in a nontwist mapping","authors":"Matheus Rolim Sales, Daniel Borin, Leonardo Costa de Souza, José Danilo Szezech Jr., Ricardo Luiz Viana, Iberê Luiz Caldas, Edson Denis Leonel","doi":"arxiv-2406.06175","DOIUrl":"https://doi.org/arxiv-2406.06175","url":null,"abstract":"We investigate the transport of particles in the chaotic component of phase\u0000space for a two-dimensional, area-preserving nontwist map. The survival\u0000probability for particles within the chaotic sea is described by an exponential\u0000decay for regions in phase space predominantly chaotic and it is scaling\u0000invariant in this case. Alternatively, when considering mixed chaotic and\u0000regular regions, there is a deviation from the exponential decay, characterized\u0000by a power law tail for long times, a signature of the stickiness effect.\u0000Furthermore, due to the asymmetry of the chaotic component of phase space with\u0000respect to the line $I = 0$, there is an unbalanced stickiness which generates\u0000a ratchet current in phase space. Finally, we perform a phenomenological\u0000description of the diffusion of chaotic particles by identifying three scaling\u0000hypotheses, and obtaining the critical exponents via extensive numerical\u0000simulations.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504255","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}
The paper presents two representative classes of Impulsive Fractional Differential Equations defined with generalized Caputo's derivative, with fixed lower limit and changing lower limit, respectively. Memory principle is studied and numerical examples are considered. The problem of the memory principle of the Matlab code for Lyapunov exponents of fractional order systems [Danca & Kuznetsov, 2018] is analyzed.
{"title":"Memory principle of the Matlab code for Lyapunov Exponents of fractional order","authors":"Marius-F. Danca, Michal feckan","doi":"arxiv-2406.04686","DOIUrl":"https://doi.org/arxiv-2406.04686","url":null,"abstract":"The paper presents two representative classes of Impulsive Fractional\u0000Differential Equations defined with generalized Caputo's derivative, with\u0000fixed lower limit and changing lower limit, respectively. Memory principle is\u0000studied and numerical examples are considered. The problem of the memory\u0000principle of the Matlab code for Lyapunov exponents of fractional order systems\u0000[Danca & Kuznetsov, 2018] is analyzed.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504256","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}
An excitation of highly nonlinear, complex magnetization dynamics in a ferromagnet, for example chaos, is a new research target in spintronics. This technology is applied to practical applications such as random number generator and information processing systems. One way to induce complex dynamics is applying feedback effect to the ferromagnet. The role of the feedback electric current on the magnetization dynamics was studied in the past. However, there is another way to apply feedback effect to the ferromagnet, namely feedback magnetic field. In this paper, we developed both numerical and theoretical analyses on the role of the feedback magnetic field causing complex magnetization dynamics. The numerical simulation indicates the change of the dynamical behavior from a simple oscillation with a unique frequency to complex dynamics such as amplitude modulation and chaos. The theoretical analyses on the equation of motion qualitatively explain several features found in the numerical simulations, exemplified as an appearance of multipeak structure in the Fourier spectra. The difference of the role of the feedback electric current and magnetic field is also revealed from the theoretical analyses.
{"title":"Chaotic magnetization dynamics driven by feedback magnetic field","authors":"Tomohiro Taniguchi","doi":"arxiv-2406.05296","DOIUrl":"https://doi.org/arxiv-2406.05296","url":null,"abstract":"An excitation of highly nonlinear, complex magnetization dynamics in a\u0000ferromagnet, for example chaos, is a new research target in spintronics. This\u0000technology is applied to practical applications such as random number generator\u0000and information processing systems. One way to induce complex dynamics is\u0000applying feedback effect to the ferromagnet. The role of the feedback electric\u0000current on the magnetization dynamics was studied in the past. However, there\u0000is another way to apply feedback effect to the ferromagnet, namely feedback\u0000magnetic field. In this paper, we developed both numerical and theoretical\u0000analyses on the role of the feedback magnetic field causing complex\u0000magnetization dynamics. The numerical simulation indicates the change of the\u0000dynamical behavior from a simple oscillation with a unique frequency to complex\u0000dynamics such as amplitude modulation and chaos. The theoretical analyses on\u0000the equation of motion qualitatively explain several features found in the\u0000numerical simulations, exemplified as an appearance of multipeak structure in\u0000the Fourier spectra. The difference of the role of the feedback electric\u0000current and magnetic field is also revealed from the theoretical analyses.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515169","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}
Matheus Rolim Sales, Daniel Borin, Diogo Ricardo da Costa, José Danilo Szezech Jr., Edson Denis Leonel
We investigate some statistical properties of escaping particles in a billiard system whose boundary is described by two control parameters with a hole on its boundary. Initially, we analyze the survival probability for different hole positions and sizes. We notice the survival probability follows an exponential decay with a characteristic power law tail when the hole is positioned partially or entirely over large stability islands in phase space. We find the survival probability exhibits scaling invariance with respect to the hole size. In contrast, the survival probability for holes placed in predominantly chaotic regions deviates from the exponential decay. We introduce two holes simultaneously and investigate the complexity of the escape basins for different hole sizes and control parameters by means of the basin entropy and the basin boundary entropy. We find a non-trivial relation between these entropies and the system's parameters and show that the basin entropy exhibits scaling invariance for a specific control parameter interval.
{"title":"An investigation of escape and scaling properties of a billiard system","authors":"Matheus Rolim Sales, Daniel Borin, Diogo Ricardo da Costa, José Danilo Szezech Jr., Edson Denis Leonel","doi":"arxiv-2406.04479","DOIUrl":"https://doi.org/arxiv-2406.04479","url":null,"abstract":"We investigate some statistical properties of escaping particles in a\u0000billiard system whose boundary is described by two control parameters with a\u0000hole on its boundary. Initially, we analyze the survival probability for\u0000different hole positions and sizes. We notice the survival probability follows\u0000an exponential decay with a characteristic power law tail when the hole is\u0000positioned partially or entirely over large stability islands in phase space.\u0000We find the survival probability exhibits scaling invariance with respect to\u0000the hole size. In contrast, the survival probability for holes placed in\u0000predominantly chaotic regions deviates from the exponential decay. We introduce\u0000two holes simultaneously and investigate the complexity of the escape basins\u0000for different hole sizes and control parameters by means of the basin entropy\u0000and the basin boundary entropy. We find a non-trivial relation between these\u0000entropies and the system's parameters and show that the basin entropy exhibits\u0000scaling invariance for a specific control parameter interval.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515170","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}
This paper investigates the dynamics and integrability of the double spring pendulum, which has great importance in studying nonlinear dynamics, chaos, and bifurcations. Being a Hamiltonian system with three degrees of freedom, its analysis presents a significant challenge. To gain insight into the system's dynamics, we employ various numerical methods, including Lyapunov exponents spectra, phase-parametric diagrams, and Poincar'e cross-sections. The novelty of our work lies in the integration of these three numerical methods into one powerful tool. We provide a comprehensive understanding of the system's dynamics by identifying parameter values or initial conditions that lead to hyper-chaotic, chaotic, quasi-periodic, and periodic motion, which is a novel contribution in the context of Hamiltonian systems. In the absence of gravitational potential, the system exhibits $S^1$ symmetry, and the presence of an additional first integral was identified using Lyapunov exponents diagrams. We demonstrate the effective utilisation of Lyapunov exponents as a potential indicator of first integrals and integrable dynamics. The numerical analysis is complemented by an analytical proof regarding the non-integrability of the system. This proof relies on the analysis of properties of the differential Galois group of variational equations along specific solutions of the system. To facilitate this analysis, we utilised a newly developed extension of the Kovacic algorithm specifically designed for fourth-order differential equations. Overall, our study sheds light on the intricate dynamics and integrability of the double spring pendulum, offering new insights and methodologies for further research in this field. The article has been published in JSV, and the final version is available at this link: https://doi.org/10.1016/j.jsv.2024.118550
{"title":"Dynamics and non-integrability of the double spring pendulum","authors":"Wojciech Szumiński, Andrzej J. Maciejewski","doi":"arxiv-2406.02200","DOIUrl":"https://doi.org/arxiv-2406.02200","url":null,"abstract":"This paper investigates the dynamics and integrability of the double spring\u0000pendulum, which has great importance in studying nonlinear dynamics, chaos, and\u0000bifurcations. Being a Hamiltonian system with three degrees of freedom, its\u0000analysis presents a significant challenge. To gain insight into the system's\u0000dynamics, we employ various numerical methods, including Lyapunov exponents\u0000spectra, phase-parametric diagrams, and Poincar'e cross-sections. The novelty\u0000of our work lies in the integration of these three numerical methods into one\u0000powerful tool. We provide a comprehensive understanding of the system's\u0000dynamics by identifying parameter values or initial conditions that lead to\u0000hyper-chaotic, chaotic, quasi-periodic, and periodic motion, which is a novel\u0000contribution in the context of Hamiltonian systems. In the absence of\u0000gravitational potential, the system exhibits $S^1$ symmetry, and the presence\u0000of an additional first integral was identified using Lyapunov exponents\u0000diagrams. We demonstrate the effective utilisation of Lyapunov exponents as a\u0000potential indicator of first integrals and integrable dynamics. The numerical\u0000analysis is complemented by an analytical proof regarding the non-integrability\u0000of the system. This proof relies on the analysis of properties of the\u0000differential Galois group of variational equations along specific solutions of\u0000the system. To facilitate this analysis, we utilised a newly developed\u0000extension of the Kovacic algorithm specifically designed for fourth-order\u0000differential equations. Overall, our study sheds light on the intricate\u0000dynamics and integrability of the double spring pendulum, offering new insights\u0000and methodologies for further research in this field. The article has been published in JSV, and the final version is available at\u0000this link: https://doi.org/10.1016/j.jsv.2024.118550","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254604","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 examine the impact of time delay on two coupled phase oscillators within the second-order Kuramoto model, which is relevant to the operations of real-world networks that rely on signal transmission speed constraints. Our analytical and numerical exploration shows that time delay can cause multi-stability within phase-locked solutions, and the stability of these solutions decreases as inertia increases. In addition to phase-locked solutions, we discovered non-phase-locked solutions that exhibit periodic and chaotic behaviors, depending on the amount of inertia and time delay. Our results suggest that this system has the potential to create patterns similar to epileptic seizures.
{"title":"Synchronization of two coupled phase oscillators in the time-delayed second-order Kuramoto model","authors":"Esmaeil Mahdavi, Mina Zarei, Farhad Shahbazi","doi":"arxiv-2406.01208","DOIUrl":"https://doi.org/arxiv-2406.01208","url":null,"abstract":"We examine the impact of time delay on two coupled phase oscillators within\u0000the second-order Kuramoto model, which is relevant to the operations of\u0000real-world networks that rely on signal transmission speed constraints. Our\u0000analytical and numerical exploration shows that time delay can cause\u0000multi-stability within phase-locked solutions, and the stability of these\u0000solutions decreases as inertia increases. In addition to phase-locked\u0000solutions, we discovered non-phase-locked solutions that exhibit periodic and\u0000chaotic behaviors, depending on the amount of inertia and time delay. Our\u0000results suggest that this system has the potential to create patterns similar\u0000to epileptic seizures.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259814","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}
Introducing disorder in a system typically breaks symmetries and can introduce dramatic changes in its properties such as localization. At the same time, the clean system can have distinct many-body features depending on how chaotic it is. In this work the effect of permutation symmetry breaking by disorder is studied in a system which has a controllable and deterministic regular to chaotic transition. Results indicate a continuous phase transition from an area-law to a volume-law entangled phase irrespective of whether there is chaos or not, as the strength of the disorder is increased. The critical disorder strength obtained by finite size scaling, indicate a strong dependence on whether the clean system is regular or chaotic to begin with. In the process, we also obtain the critical exponents associated with this phase transition. Additionally, we find that a relatively small disorder is seen to be sufficient to delocalize a chaotic system.
{"title":"Chaos controlled and disorder driven phase transitions by breaking permutation symmetry","authors":"Manju C, Arul Lakshminarayan, Uma Divakaran","doi":"arxiv-2406.00521","DOIUrl":"https://doi.org/arxiv-2406.00521","url":null,"abstract":"Introducing disorder in a system typically breaks symmetries and can\u0000introduce dramatic changes in its properties such as localization. At the same\u0000time, the clean system can have distinct many-body features depending on how\u0000chaotic it is. In this work the effect of permutation symmetry breaking by\u0000disorder is studied in a system which has a controllable and deterministic\u0000regular to chaotic transition. Results indicate a continuous phase transition\u0000from an area-law to a volume-law entangled phase irrespective of whether there\u0000is chaos or not, as the strength of the disorder is increased. The critical\u0000disorder strength obtained by finite size scaling, indicate a strong dependence\u0000on whether the clean system is regular or chaotic to begin with. In the\u0000process, we also obtain the critical exponents associated with this phase\u0000transition. Additionally, we find that a relatively small disorder is seen to\u0000be sufficient to delocalize a chaotic system.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"355 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515171","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}
Successive image generation using cyclic transformations is demonstrated by extending the CycleGAN model to transform images among three different categories. Repeated application of the trained generators produces sequences of images that transition among the different categories. The generated image sequences occupy a more limited region of the image space compared with the original training dataset. Quantitative evaluation using precision and recall metrics indicates that the generated images have high quality but reduced diversity relative to the training dataset. Such successive generation processes are characterized as chaotic dynamics in terms of dynamical system theory. Positive Lyapunov exponents estimated from the generated trajectories confirm the presence of chaotic dynamics, with the Lyapunov dimension of the attractor found to be comparable to the intrinsic dimension of the training data manifold. The results suggest that chaotic dynamics in the image space defined by the deep generative model contribute to the diversity of the generated images, constituting a novel approach for multi-class image generation. This model can be interpreted as an extension of classical associative memory to perform hetero-association among image categories.
{"title":"Cyclic image generation using chaotic dynamics","authors":"Takaya Tanaka, Yutaka Yamaguti","doi":"arxiv-2405.20717","DOIUrl":"https://doi.org/arxiv-2405.20717","url":null,"abstract":"Successive image generation using cyclic transformations is demonstrated by\u0000extending the CycleGAN model to transform images among three different\u0000categories. Repeated application of the trained generators produces sequences\u0000of images that transition among the different categories. The generated image\u0000sequences occupy a more limited region of the image space compared with the\u0000original training dataset. Quantitative evaluation using precision and recall\u0000metrics indicates that the generated images have high quality but reduced\u0000diversity relative to the training dataset. Such successive generation\u0000processes are characterized as chaotic dynamics in terms of dynamical system\u0000theory. Positive Lyapunov exponents estimated from the generated trajectories\u0000confirm the presence of chaotic dynamics, with the Lyapunov dimension of the\u0000attractor found to be comparable to the intrinsic dimension of the training\u0000data manifold. The results suggest that chaotic dynamics in the image space\u0000defined by the deep generative model contribute to the diversity of the\u0000generated images, constituting a novel approach for multi-class image\u0000generation. This model can be interpreted as an extension of classical\u0000associative memory to perform hetero-association among image categories.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254876","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：