E. da Hora, L. Pereira, C. dos Santos, F. C. Simas
We consider an enlarged $(1+1)$-dimensional model with two real scalar fields, $phi$ and $chi$ whose scalar potential $V(phi,chi)$ has a standard $chi^4$ sector and a sine-Gordon one for $phi$. These fields are coupled through a generalizing function $f(chi)$ that appears in the scalar potential and controls the nontrivial dynamics of $phi$. We minimize the effective energy via the implementation of the BPS technique. We then obtain the Bogomol'nyi bound for the energy and the first-order equations whose solutions saturate that bound. We solve these equations for a nontrivial $f(chi)$. As the result, BPS kinks with internal structures emerge. They exhibit a two-kink profile. i.e. an effect due to geometrical constrictions. We consider the linear stability of these new configurations. In this sense, we study the existence of internal modes that play an important role during the scattering process. We then investigate the kink-antikink collisions, and present the numerical results for the most interesting cases. We also comment about their most relevant features.
{"title":"Geometrically constrained sine-Gordon field: BPS solitons and their collisions","authors":"E. da Hora, L. Pereira, C. dos Santos, F. C. Simas","doi":"arxiv-2409.09767","DOIUrl":"https://doi.org/arxiv-2409.09767","url":null,"abstract":"We consider an enlarged $(1+1)$-dimensional model with two real scalar\u0000fields, $phi$ and $chi$ whose scalar potential $V(phi,chi)$ has a standard\u0000$chi^4$ sector and a sine-Gordon one for $phi$. These fields are coupled\u0000through a generalizing function $f(chi)$ that appears in the scalar potential\u0000and controls the nontrivial dynamics of $phi$. We minimize the effective\u0000energy via the implementation of the BPS technique. We then obtain the\u0000Bogomol'nyi bound for the energy and the first-order equations whose solutions\u0000saturate that bound. We solve these equations for a nontrivial $f(chi)$. As\u0000the result, BPS kinks with internal structures emerge. They exhibit a two-kink\u0000profile. i.e. an effect due to geometrical constrictions. We consider the\u0000linear stability of these new configurations. In this sense, we study the\u0000existence of internal modes that play an important role during the scattering\u0000process. We then investigate the kink-antikink collisions, and present the\u0000numerical results for the most interesting cases. We also comment about their\u0000most relevant features.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267933","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}
Symbiotic vortex-bright soliton structures with non-trivial topological charge in one component are found to be robust in immiscibel two-component superfluids, due to the effective potential created by a stable vortex in the other component. We explore the properties of symbiotic vortex-bright soliton in strongly coupled binary superfluids by holography, which naturally incorporates finite temperature effect and dissipation. We show the dependence of the configuration on various parameters, including the winding number, temperature and inter-component coupling. We then study the (in)stability of symbiotic vortex-bright soliton by both the linear approach via quasi-normal modes and the full non-linear numerical simulation. Rich dynamics are found for the splitting patterns and dynamical transitions. Moreover, for giant symbiotic vortex-bright soliton structures with large winding numbers, the vortex splitting instability might be rooted in the Kelvin-Helmholtz instability. We also show that the second component in the vortex core could act as a stabilizer so as to suppress or even prevent vortex splitting instability. Such stabilization mechanism opens possibility for vortices with smaller winding number to merge into vortices with larger winding number, which is confirmed for the first time in our simulation.
{"title":"(In)stability of symbiotic vortex-bright soliton in holographic immiscible binary superfluids","authors":"Yuping An, Li Li","doi":"arxiv-2409.08310","DOIUrl":"https://doi.org/arxiv-2409.08310","url":null,"abstract":"Symbiotic vortex-bright soliton structures with non-trivial topological\u0000charge in one component are found to be robust in immiscibel two-component\u0000superfluids, due to the effective potential created by a stable vortex in the\u0000other component. We explore the properties of symbiotic vortex-bright soliton\u0000in strongly coupled binary superfluids by holography, which naturally\u0000incorporates finite temperature effect and dissipation. We show the dependence\u0000of the configuration on various parameters, including the winding number,\u0000temperature and inter-component coupling. We then study the (in)stability of\u0000symbiotic vortex-bright soliton by both the linear approach via quasi-normal\u0000modes and the full non-linear numerical simulation. Rich dynamics are found for\u0000the splitting patterns and dynamical transitions. Moreover, for giant symbiotic\u0000vortex-bright soliton structures with large winding numbers, the vortex\u0000splitting instability might be rooted in the Kelvin-Helmholtz instability. We\u0000also show that the second component in the vortex core could act as a\u0000stabilizer so as to suppress or even prevent vortex splitting instability. Such\u0000stabilization mechanism opens possibility for vortices with smaller winding\u0000number to merge into vortices with larger winding number, which is confirmed\u0000for the first time in our simulation.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267934","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}
Mahamat Abdoulaye Adamdine, Venceslas Nguefoue Meli, Steve J. Kongni, Thierry Njougouo, Patrick Louodop
This study delves into the emergence of collective behaviors within a network comprising interacting cells. Each cell integrates a fixed number of neurons governed by an activation gradient based on Hopfield's model. The intra-cell interactions among neurons are local and directed, while inter-cell connections are facilitated through a PID (Proportional-Integral-Derivative) coupling mechanism. This coupling introduces an adaptable environmental variable, influencing the network dynamics significantly. Numerical simulations employing three neurons per cell across a network of fifty cells reveal diverse dynamics, including incoherence, coherence, synchronization, chimera states, and traveling wave. These phenomena are quantitatively assessed using statistical measures such as the order parameter, strength of incoherence, and discontinuity measure. Variations of the resistive, inductive, or capacitive couplings of the inter-cell environment are explored and their effects are analysed. Furthermore, the study identifies multistability in network dynamics, characterized by the coexistence of multiple stable states for the same set of parameters but with different initial conditions. A linear augmentation strategy is employed for its control.
{"title":"Chimera state in neural network with the PID coupling","authors":"Mahamat Abdoulaye Adamdine, Venceslas Nguefoue Meli, Steve J. Kongni, Thierry Njougouo, Patrick Louodop","doi":"arxiv-2409.07624","DOIUrl":"https://doi.org/arxiv-2409.07624","url":null,"abstract":"This study delves into the emergence of collective behaviors within a network\u0000comprising interacting cells. Each cell integrates a fixed number of neurons\u0000governed by an activation gradient based on Hopfield's model. The intra-cell\u0000interactions among neurons are local and directed, while inter-cell connections\u0000are facilitated through a PID (Proportional-Integral-Derivative) coupling\u0000mechanism. This coupling introduces an adaptable environmental variable,\u0000influencing the network dynamics significantly. Numerical simulations employing\u0000three neurons per cell across a network of fifty cells reveal diverse dynamics,\u0000including incoherence, coherence, synchronization, chimera states, and\u0000traveling wave. These phenomena are quantitatively assessed using statistical\u0000measures such as the order parameter, strength of incoherence, and\u0000discontinuity measure. Variations of the resistive, inductive, or capacitive\u0000couplings of the inter-cell environment are explored and their effects are\u0000analysed. Furthermore, the study identifies multistability in network dynamics,\u0000characterized by the coexistence of multiple stable states for the same set of\u0000parameters but with different initial conditions. A linear augmentation\u0000strategy is employed for its control.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227120","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}
Edgardo Villar-Sepúlveda, Alan R. Champneys, Andrew L. Krause
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with specific features, but the case of non-diagonal diffusion matrices has yet to be analysed. Here, a framework is presented for the design of general $n$-component reaction-cross-diffusion systems that exhibit Turing and wave instabilities of a given wavelength. For a fixed set of reaction kinetics, it is shown how to choose diffusion matrices that produce each instability; conversely, for a given diffusion tensor, how to choose linearised kinetics. The theory is applied to several examples including a hyperbolic reaction-diffusion system, two different 3-component models, and a spatio-temporal version of the Ross-Macdonald model for the spread of malaria.
{"title":"Designing reaction-cross-diffusion systems with Turing and wave instabilities","authors":"Edgardo Villar-Sepúlveda, Alan R. Champneys, Andrew L. Krause","doi":"arxiv-2409.06860","DOIUrl":"https://doi.org/arxiv-2409.06860","url":null,"abstract":"General conditions are established under which reaction-cross-diffusion\u0000systems can undergo spatiotemporal pattern-forming instabilities. Recent work\u0000has focused on designing systems theoretically and experimentally to exhibit\u0000patterns with specific features, but the case of non-diagonal diffusion\u0000matrices has yet to be analysed. Here, a framework is presented for the design\u0000of general $n$-component reaction-cross-diffusion systems that exhibit Turing\u0000and wave instabilities of a given wavelength. For a fixed set of reaction\u0000kinetics, it is shown how to choose diffusion matrices that produce each\u0000instability; conversely, for a given diffusion tensor, how to choose linearised\u0000kinetics. The theory is applied to several examples including a hyperbolic\u0000reaction-diffusion system, two different 3-component models, and a\u0000spatio-temporal version of the Ross-Macdonald model for the spread of malaria.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217298","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}
Edgardo Villar-Sepúlveda, Alan R. Champneys, Davide Cusseddu, Anotida Madzvamuse
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of $n$-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk. Linear analysis shows conditions under which various pattern modes can become unstable to either generalised pitchfork or transcritical bifurcations depending on the parity of the spatial wavenumber. Weakly nonlinear analysis is used to derive general expressions for the multi-component amplitude equations of different patterned states. These reduced-order systems are found to agree with prior normal forms for pattern formation bifurcations with $O(3)$ symmetry and provide information on the stability of bifurcating patterns of different symmetry types. The analysis is complemented with numerical results using a dedicated finite-element method. The theory is illustrated in two examples; a bulk-surface version of the Brusselator, and a four-component cell-polarity model.
{"title":"Pattern formation of bulk-surface reaction-diffusion systems in a ball","authors":"Edgardo Villar-Sepúlveda, Alan R. Champneys, Davide Cusseddu, Anotida Madzvamuse","doi":"arxiv-2409.06826","DOIUrl":"https://doi.org/arxiv-2409.06826","url":null,"abstract":"Weakly nonlinear amplitude equations are derived for the onset of spatially\u0000extended patterns on a general class of $n$-component bulk-surface\u0000reaction-diffusion systems in a ball, under the assumption of linear kinetics\u0000in the bulk. Linear analysis shows conditions under which various pattern modes\u0000can become unstable to either generalised pitchfork or transcritical\u0000bifurcations depending on the parity of the spatial wavenumber. Weakly\u0000nonlinear analysis is used to derive general expressions for the\u0000multi-component amplitude equations of different patterned states. These\u0000reduced-order systems are found to agree with prior normal forms for pattern\u0000formation bifurcations with $O(3)$ symmetry and provide information on the\u0000stability of bifurcating patterns of different symmetry types. The analysis is\u0000complemented with numerical results using a dedicated finite-element method.\u0000The theory is illustrated in two examples; a bulk-surface version of the\u0000Brusselator, and a four-component cell-polarity model.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217294","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}
Tomasz Dobrowolski, Jacek Gatlik, Panayotis G. Kevrekidis
The behavior of the kink in the sine-Gordon (sG) model in the presence of periodic inhomogeneity is studied. An ansatz is proposed that allows for the construction of a reliable effective model with two degrees of freedom. Effective models with excellent agreement with the original field-theoretic partial differential equation are constructed, including in the non-perturbative region and for relativistic velocities. The numerical solutions of the sG model describing the evolution of the kink in the presence of a barrier as well as in the case of a periodic heterogeneity under the potential additional influence of a switched bias current and/or dissipation were obtained. The results of the field equation and the effective models were compared. The effect of the choice of initial conditions in the field model on the agreement of the results with the effective model is discussed.
{"title":"Kink movement on a periodic background","authors":"Tomasz Dobrowolski, Jacek Gatlik, Panayotis G. Kevrekidis","doi":"arxiv-2409.05436","DOIUrl":"https://doi.org/arxiv-2409.05436","url":null,"abstract":"The behavior of the kink in the sine-Gordon (sG) model in the presence of\u0000periodic inhomogeneity is studied. An ansatz is proposed that allows for the\u0000construction of a reliable effective model with two degrees of freedom.\u0000Effective models with excellent agreement with the original field-theoretic\u0000partial differential equation are constructed, including in the\u0000non-perturbative region and for relativistic velocities. The numerical\u0000solutions of the sG model describing the evolution of the kink in the presence\u0000of a barrier as well as in the case of a periodic heterogeneity under the\u0000potential additional influence of a switched bias current and/or dissipation\u0000were obtained. The results of the field equation and the effective models were\u0000compared. The effect of the choice of initial conditions in the field model on\u0000the agreement of the results with the effective model is discussed.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217317","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}
M. M. Terzi, O. U. Salman, D. Faurie, A. A. León Baldelli
In phase-field theories of brittle fracture, crack initiation, growth and path selection are investigated using non-convex energy functionals and a stability criterion. The lack of convexity with respect to the state poses difficulties to monolithic solvers that aim to solve for kinematic and internal variables, simultaneously. In this paper, we inquire into the effectiveness of quasi-Newton algorithms as an alternative to conventional Newton-Raphson solvers. These algorithms improve convergence by constructing a positive definite approximation of the Hessian, bargaining improved convergence with the risk of missing bifurcation points and stability thresholds. Our study focuses on one-dimensional phase-field fracture models of brittle thin films on elastic foundations. Within this framework, in the absence of irreversibility constraint, we construct an equilibrium map that represents all stable and unstable equilibrium states as a function of the external load, using well-known branch-following bifurcation techniques. Our main finding is that quasi-Newton algorithms fail to select stable evolution paths without exact second variation information. To solve this issue, we perform a spectral analysis of the full Hessian, providing optimal perturbations that enable quasi-Newton methods to follow a stable and potentially unique path for crack evolution. Finally, we discuss the stability issues and optimal perturbations in the case when the damage irreversibility is present, changing the topological structure of the set of admissible perturbations from a linear vector space to a convex cone.
{"title":"Navigating with Stability: Local Minima, Patterns, and Evolution in a Gradient Damage Fracture Model","authors":"M. M. Terzi, O. U. Salman, D. Faurie, A. A. León Baldelli","doi":"arxiv-2409.04307","DOIUrl":"https://doi.org/arxiv-2409.04307","url":null,"abstract":"In phase-field theories of brittle fracture, crack initiation, growth and\u0000path selection are investigated using non-convex energy functionals and a\u0000stability criterion. The lack of convexity with respect to the state poses\u0000difficulties to monolithic solvers that aim to solve for kinematic and internal\u0000variables, simultaneously. In this paper, we inquire into the effectiveness of\u0000quasi-Newton algorithms as an alternative to conventional Newton-Raphson\u0000solvers. These algorithms improve convergence by constructing a positive\u0000definite approximation of the Hessian, bargaining improved convergence with the\u0000risk of missing bifurcation points and stability thresholds. Our study focuses\u0000on one-dimensional phase-field fracture models of brittle thin films on elastic\u0000foundations. Within this framework, in the absence of irreversibility\u0000constraint, we construct an equilibrium map that represents all stable and\u0000unstable equilibrium states as a function of the external load, using\u0000well-known branch-following bifurcation techniques. Our main finding is that\u0000quasi-Newton algorithms fail to select stable evolution paths without exact\u0000second variation information. To solve this issue, we perform a spectral\u0000analysis of the full Hessian, providing optimal perturbations that enable\u0000quasi-Newton methods to follow a stable and potentially unique path for crack\u0000evolution. Finally, we discuss the stability issues and optimal perturbations\u0000in the case when the damage irreversibility is present, changing the\u0000topological structure of the set of admissible perturbations from a linear\u0000vector space to a convex cone.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217295","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 interplay between topology and soliton is a central topic in nonlinear topological physics. So far, most studies have been confined to conservative settings. Here, we explore Thouless pumping of dissipative temporal solitons in a nonconservative one-dimensional optical system with gain and spectral filtering, described by the paradigmatic complex Ginzburg-Landau equation. Two dissipatively induced nonlinear topological phase transitions are identified. First, when varying dissipative parameters across a threshold, the soliton transitions from being trapped in time to quantized drifting. This quantized temporal drift remains robust, even as the system evolves from a single-soliton state into multi-soliton state. Second, a dynamically emergent phase transition is found: the soliton is arrested until a critical point of its evolution, where a transition to topological drift occurs. Both phenomena uniquely arise from the dynamical interplay of dissipation, nonlinearity and topology.
{"title":"Dissipative Nonlinear Thouless Pumping of Temporal Solitons","authors":"Xuzhen Cao, Chunyu Jia, Ying Hu, Zhaoxin Liang","doi":"arxiv-2409.03450","DOIUrl":"https://doi.org/arxiv-2409.03450","url":null,"abstract":"The interplay between topology and soliton is a central topic in nonlinear\u0000topological physics. So far, most studies have been confined to conservative\u0000settings. Here, we explore Thouless pumping of dissipative temporal solitons in\u0000a nonconservative one-dimensional optical system with gain and spectral\u0000filtering, described by the paradigmatic complex Ginzburg-Landau equation. Two\u0000dissipatively induced nonlinear topological phase transitions are identified.\u0000First, when varying dissipative parameters across a threshold, the soliton\u0000transitions from being trapped in time to quantized drifting. This quantized\u0000temporal drift remains robust, even as the system evolves from a single-soliton\u0000state into multi-soliton state. Second, a dynamically emergent phase transition\u0000is found: the soliton is arrested until a critical point of its evolution,\u0000where a transition to topological drift occurs. Both phenomena uniquely arise\u0000from the dynamical interplay of dissipation, nonlinearity and topology.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"319 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227119","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 analytically and numerically study three-component rogue waves (RWs) in spin-1 Bose-Einstein condensates with Raman-induced spin-orbit coupling (SOC). Using the multiscale perturbative method, we obtain approximate analytical solutions for RWs with positive and negative effective masses, determined by the effective dispersion of the system. The solutions include RWs with smooth and striped shapes, as well as higher-order RWs. The analytical solutions demonstrate that the RWs in the three components of the system exhibit different velocities and their maximum peaks appear at the same spatiotemporal position, which is caused by SOC and interactions. The accuracy of the approximate analytical solutions is corroborated by comparison with direct numerical simulations of the underlying system. Additionally, we systematically explore existence domains for the RWs determined by the baseband modulational instability (BMI). Numerical simulations corroborate that, under the action of BMI, plane waves with random initial perturbations excite RWs, as predicted by the approximate analytical solutions.
{"title":"Vector rogue waves in spin-1 Bose-Einstein condensates with spin-orbit coupling","authors":"Jun-Tao He, Hui-Jun Li, Ji Lin, Boris A. Malomed","doi":"arxiv-2409.01613","DOIUrl":"https://doi.org/arxiv-2409.01613","url":null,"abstract":"We analytically and numerically study three-component rogue waves (RWs) in\u0000spin-1 Bose-Einstein condensates with Raman-induced spin-orbit coupling (SOC).\u0000Using the multiscale perturbative method, we obtain approximate analytical\u0000solutions for RWs with positive and negative effective masses, determined by\u0000the effective dispersion of the system. The solutions include RWs with smooth\u0000and striped shapes, as well as higher-order RWs. The analytical solutions\u0000demonstrate that the RWs in the three components of the system exhibit\u0000different velocities and their maximum peaks appear at the same spatiotemporal\u0000position, which is caused by SOC and interactions. The accuracy of the\u0000approximate analytical solutions is corroborated by comparison with direct\u0000numerical simulations of the underlying system. Additionally, we systematically\u0000explore existence domains for the RWs determined by the baseband modulational\u0000instability (BMI). Numerical simulations corroborate that, under the action of\u0000BMI, plane waves with random initial perturbations excite RWs, as predicted by\u0000the approximate analytical solutions.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217296","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}
Yael Avni, Michel Fruchart, David Martin, Daniel Seara, Vincenzo Vitelli
Non-reciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit, as well as the criticality of the phase transition from static to time-dependent states remains an open question. To tackle these questions, we study a minimalistic system endowed with non-reciprocal interactions: an Ising model with two spin species having opposing goals. The mean-field equation predicts three stable phases: disordered, ordered, and a time-dependent swap phase. Large scale numerical simulations support the following: (i) in 2D, the swap phase is destabilized by defects; (ii) in 3D, the swap phase is stable, and has the properties of a time-crystal; (iii) the transition from disorder to swap in 3D is characterized by the critical exponents of the 3D XY model, in agreement with the emerging continuous symmetry of time translation invariance; (iv) when the two species have fully anti-symmetric couplings, the static-order phase is unstable in any dimension due to droplet growth; (v) in the general case of asymmetric couplings, static order can be restored by a droplet-capture mechanism preventing the droplets from growing indefinitely. We provide details on the full phase diagram which includes first- and second-order-like phase transitions and study the coarsening dynamics of the swap as well as the static-order phases.
{"title":"Dynamical phase transitions in the non-reciprocal Ising model","authors":"Yael Avni, Michel Fruchart, David Martin, Daniel Seara, Vincenzo Vitelli","doi":"arxiv-2409.07481","DOIUrl":"https://doi.org/arxiv-2409.07481","url":null,"abstract":"Non-reciprocal interactions in many-body systems lead to time-dependent\u0000states, commonly observed in biological, chemical, and ecological systems. The\u0000stability of these states in the thermodynamic limit, as well as the\u0000criticality of the phase transition from static to time-dependent states\u0000remains an open question. To tackle these questions, we study a minimalistic\u0000system endowed with non-reciprocal interactions: an Ising model with two spin\u0000species having opposing goals. The mean-field equation predicts three stable\u0000phases: disordered, ordered, and a time-dependent swap phase. Large scale\u0000numerical simulations support the following: (i) in 2D, the swap phase is\u0000destabilized by defects; (ii) in 3D, the swap phase is stable, and has the\u0000properties of a time-crystal; (iii) the transition from disorder to swap in 3D\u0000is characterized by the critical exponents of the 3D XY model, in agreement\u0000with the emerging continuous symmetry of time translation invariance; (iv) when\u0000the two species have fully anti-symmetric couplings, the static-order phase is\u0000unstable in any dimension due to droplet growth; (v) in the general case of\u0000asymmetric couplings, static order can be restored by a droplet-capture\u0000mechanism preventing the droplets from growing indefinitely. We provide details\u0000on the full phase diagram which includes first- and second-order-like phase\u0000transitions and study the coarsening dynamics of the swap as well as the\u0000static-order phases.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217302","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}
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