Martin Brandenbourger, Oleksandr Gamayun, Jonas Veenstra, Freek van Gorp, Hans Terwisscha-Dekker, Jean-Sébastien Caux, Corentin Coulais
Breathing solitons consist of a fast beating wave within a compact envelope of stable shape and velocity. They manifest themselves in a variety of contexts such as plasmas, optical fibers and cold atoms, but have remained elusive when energy conservation is broken. Here, we report on the observation of breathing, unidirectional, arbitrarily long-lived solitons in non-reciprocal, non-conservative active metamaterials. Combining precision desktop experiments, numerical simulations and perturbation theory on generalizations of the sine-Gordon and nonlinear Schr"odinger equations, we demonstrate that unidirectional breathers generically emerge in weakly nonlinear non-reciprocal materials, and that their dynamics are governed by an unstable fixed point. Crucially, breathing solitons can persist for arbitrarily long times provided: (i) this fixed point displays a bifurcation upon reachin a delicate balance between energy injection and dissipation; (ii) the initial conditions allow the dynamics to reach this bifurcation point. Our work establishes non-reciprocity as a promising avenue to generate stable nonlinear unidirectional waves, and could be generalized beyond metamaterials to optics, soft matter and superconducting circuits.
{"title":"Non-reciprocal breathing solitons","authors":"Martin Brandenbourger, Oleksandr Gamayun, Jonas Veenstra, Freek van Gorp, Hans Terwisscha-Dekker, Jean-Sébastien Caux, Corentin Coulais","doi":"arxiv-2405.10562","DOIUrl":"https://doi.org/arxiv-2405.10562","url":null,"abstract":"Breathing solitons consist of a fast beating wave within a compact envelope\u0000of stable shape and velocity. They manifest themselves in a variety of contexts\u0000such as plasmas, optical fibers and cold atoms, but have remained elusive when\u0000energy conservation is broken. Here, we report on the observation of breathing,\u0000unidirectional, arbitrarily long-lived solitons in non-reciprocal,\u0000non-conservative active metamaterials. Combining precision desktop experiments,\u0000numerical simulations and perturbation theory on generalizations of the\u0000sine-Gordon and nonlinear Schr\"odinger equations, we demonstrate that\u0000unidirectional breathers generically emerge in weakly nonlinear non-reciprocal\u0000materials, and that their dynamics are governed by an unstable fixed point.\u0000Crucially, breathing solitons can persist for arbitrarily long times provided:\u0000(i) this fixed point displays a bifurcation upon reachin a delicate balance\u0000between energy injection and dissipation; (ii) the initial conditions allow the\u0000dynamics to reach this bifurcation point. Our work establishes non-reciprocity\u0000as a promising avenue to generate stable nonlinear unidirectional waves, and\u0000could be generalized beyond metamaterials to optics, soft matter and\u0000superconducting circuits.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151344","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}
Huawei Fan, Yafeng Wang, Yao Du, Haibo Qiu, Xingang Wang
Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the other oscillators remain desynchronized. Interestingly, with the increase of the coupling strength, the cluster is expanding gradually by recruiting the desynchronized oscillators one by one. This new synchronization phenomenon, which is named ``scalable synchronization cluster", is explored theoretically by the method of eigenvector-based analysis, and it is revealed that the scalability of the cluster is attributed to the unique feature of the eigenvectors of the network coupling matrix. The transient dynamics of the cluster in response to random perturbations are also studied, and it is shown that in restoring to the synchronization state, oscillators inside the cluster are stabilized in sequence, illustrating again the hierarchy of the oscillators. The findings shed new light on the collective behaviors of networked chaotic oscillators, and are helpful for the design of real-world networks where scalable synchronization clusters are concerned.
{"title":"Scalable synchronization cluster in networked chaotic oscillators","authors":"Huawei Fan, Yafeng Wang, Yao Du, Haibo Qiu, Xingang Wang","doi":"arxiv-2405.08844","DOIUrl":"https://doi.org/arxiv-2405.08844","url":null,"abstract":"Cluster synchronization in synthetic networks of coupled chaotic oscillators\u0000is investigated. It is found that despite the asymmetric nature of the network\u0000structure, a subset of the oscillators can be synchronized as a cluster while\u0000the other oscillators remain desynchronized. Interestingly, with the increase\u0000of the coupling strength, the cluster is expanding gradually by recruiting the\u0000desynchronized oscillators one by one. This new synchronization phenomenon,\u0000which is named ``scalable synchronization cluster\", is explored theoretically\u0000by the method of eigenvector-based analysis, and it is revealed that the\u0000scalability of the cluster is attributed to the unique feature of the\u0000eigenvectors of the network coupling matrix. The transient dynamics of the\u0000cluster in response to random perturbations are also studied, and it is shown\u0000that in restoring to the synchronization state, oscillators inside the cluster\u0000are stabilized in sequence, illustrating again the hierarchy of the\u0000oscillators. The findings shed new light on the collective behaviors of\u0000networked chaotic oscillators, and are helpful for the design of real-world\u0000networks where scalable synchronization clusters are concerned.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060708","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}
Static soliton bound states in nonlinear systems are investigated analytically and numerically in the framework of the parametrically driven, damped nonlinear Schr"odinger equation. We find that the ordinary differential equations, which determine bound soliton solutions, can be transformed into the form resembling the Schr"odinger-like equations for eigenfunctions with the fixed eigenvalues. We assume that a nonlinear part of the equations is close to the reflectionless potential well occurring in the scattering problem, associated with the integrable equations. We show that symmetric two-hump soliton solution is quite well described analytically by the three-soliton formula with the fixed soliton parameters, depending on the strength of parametric pumping and the dissipation constant.
{"title":"Fine structure of soliton bound states in the parametrically driven, damped nonlinear Schrödinger equation","authors":"M. M. Bogdan, O. V. Charkina","doi":"arxiv-2405.06987","DOIUrl":"https://doi.org/arxiv-2405.06987","url":null,"abstract":"Static soliton bound states in nonlinear systems are investigated\u0000analytically and numerically in the framework of the parametrically driven,\u0000damped nonlinear Schr\"odinger equation. We find that the ordinary differential\u0000equations, which determine bound soliton solutions, can be transformed into the\u0000form resembling the Schr\"odinger-like equations for eigenfunctions with the\u0000fixed eigenvalues. We assume that a nonlinear part of the equations is close to\u0000the reflectionless potential well occurring in the scattering problem,\u0000associated with the integrable equations. We show that symmetric two-hump\u0000soliton solution is quite well described analytically by the three-soliton\u0000formula with the fixed soliton parameters, depending on the strength of\u0000parametric pumping and the dissipation constant.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938201","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}
Previously, a class of regular and asymptotically flat gravitating scalar solitons (scalarons) has been constructed in the Einstein--Klein--Gordon (EKG) theory by adopting a phantom field with Higgs-like potential where the kinetic term has the wrong sign and the scalaron possesses the negative Arnowitt--Deser--Misner (ADM) mass as a consequence. In this paper, we demonstrate that the use of the phantom field can be avoided by inverting the Higgs-like potential in the EKG system when the kinetic term has a proper sign, such that the corresponding gravitating scalaron can possess the positive ADM mass. We systematically study the basic properties of the gravitating scalaron, such as the ADM mass, the energy conditions, the geodesics of test particles, etc. Moreover, we find that it can be smoothly connected to the counterpart hairy black hole solutions from our recent work in the small horizon limit.
{"title":"Gravitating Scalarons with Inverted Higgs Potential","authors":"Xiao Yan Chew, Kok-Geng Lim","doi":"arxiv-2405.06407","DOIUrl":"https://doi.org/arxiv-2405.06407","url":null,"abstract":"Previously, a class of regular and asymptotically flat gravitating scalar\u0000solitons (scalarons) has been constructed in the Einstein--Klein--Gordon (EKG)\u0000theory by adopting a phantom field with Higgs-like potential where the kinetic\u0000term has the wrong sign and the scalaron possesses the negative\u0000Arnowitt--Deser--Misner (ADM) mass as a consequence. In this paper, we\u0000demonstrate that the use of the phantom field can be avoided by inverting the\u0000Higgs-like potential in the EKG system when the kinetic term has a proper sign,\u0000such that the corresponding gravitating scalaron can possess the positive ADM\u0000mass. We systematically study the basic properties of the gravitating scalaron,\u0000such as the ADM mass, the energy conditions, the geodesics of test particles,\u0000etc. Moreover, we find that it can be smoothly connected to the counterpart\u0000hairy black hole solutions from our recent work in the small horizon limit.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938127","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 provides an analytical and numerical investigation of the dynamics of a one-dimensional chain of coupled optical resonators with conservative cubic nonlinearity and the gain saturated by nonlinear losses. The linear dependency of the resonator eigenfrequencies on their indexes makes it possible to use Wannier-Stark states as lasing modes. Numerical simulations have shown that the dependency of the resonant frequencies on the light intensity strongly affects the stability of Wannier-Stark states. To explain the observed destabilization of monochromatic lasing based on Wannier-Stark states a simple perturbation theory has been developed and compared with the data obtained in the numerical simulations.
{"title":"Kerr nonlinearity effect on the stability of Wannier-Stark states in active optical systems","authors":"Alexey Verbitskiy, Alexey Yulin","doi":"arxiv-2405.05018","DOIUrl":"https://doi.org/arxiv-2405.05018","url":null,"abstract":"The paper provides an analytical and numerical investigation of the dynamics\u0000of a one-dimensional chain of coupled optical resonators with conservative\u0000cubic nonlinearity and the gain saturated by nonlinear losses. The linear\u0000dependency of the resonator eigenfrequencies on their indexes makes it possible\u0000to use Wannier-Stark states as lasing modes. Numerical simulations have shown\u0000that the dependency of the resonant frequencies on the light intensity strongly\u0000affects the stability of Wannier-Stark states. To explain the observed\u0000destabilization of monochromatic lasing based on Wannier-Stark states a simple\u0000perturbation theory has been developed and compared with the data obtained in\u0000the numerical simulations.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938072","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}
In this work, we demonstrate that the synergetic interplay of topology, nonreciprocity and nonlinearity is capable of unprecedented effects. We focus on a nonreciprocal variant of the Su-Shrieffer-Heeger chain with local Kerr nonlinearity. We find a continuous family of non-reciprocal edge solitons (NESs) emerging from the topological edge mode, with near-zero energy, in great contrast from their reciprocal counterparts. Analytical results show that this energy decays exponentially towards zero when increasing the lattice size. Consequently, despite the absence of chiral symmetry within the system, we obtain zero-energy NESs, which are insensitive to growing Kerr nonlinearity. Even more surprising, these zero-energy NESs also persist in the strong nonlinear limit. Our work may enable new avenues for the control of nonlinear topological waves without requiring the addition of complex chiral-preserving nonlinearities.
{"title":"Insensitive edge solitons in non-Hermitian topological lattices","authors":"Bertin Many Manda, Vassos Achilleos","doi":"arxiv-2405.05441","DOIUrl":"https://doi.org/arxiv-2405.05441","url":null,"abstract":"In this work, we demonstrate that the synergetic interplay of topology,\u0000nonreciprocity and nonlinearity is capable of unprecedented effects. We focus\u0000on a nonreciprocal variant of the Su-Shrieffer-Heeger chain with local Kerr\u0000nonlinearity. We find a continuous family of non-reciprocal edge solitons\u0000(NESs) emerging from the topological edge mode, with near-zero energy, in great\u0000contrast from their reciprocal counterparts. Analytical results show that this\u0000energy decays exponentially towards zero when increasing the lattice size.\u0000Consequently, despite the absence of chiral symmetry within the system, we\u0000obtain zero-energy NESs, which are insensitive to growing Kerr nonlinearity.\u0000Even more surprising, these zero-energy NESs also persist in the strong\u0000nonlinear limit. Our work may enable new avenues for the control of nonlinear\u0000topological waves without requiring the addition of complex chiral-preserving\u0000nonlinearities.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938073","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 use Riemann problem for soliton gas as a benchmark for a detailed numerical validation of the spectral kinetic theory for the Korteweg-de Vries (KdV) and the focusing nonlinear Schr"odinger (fNLS) equations. We construct weak solutions to the kinetic equation for soliton gas describing collision of two dense "polychromatic" soliton gases composed of a finite number of "monochromatic" components, each consisting of solitons with nearly identical spectral parameters of the scattering operator in the Lax pair. The interaction between the gas components plays the key role in the emergent, large-scale hydrodynamic evolution. We then use the solutions of the spectral kinetic equation to evaluate macroscopic physical observables in KdV and fNLS soliton gases and compare them with the respective ensemble averages extracted from the "exact" soliton gas numerical solutions of the KdV and fNLS equations. To numerically synthesise dense polychromatic soliton gases we develop a new method which combines recent advances in the spectral theory of the so-called soliton condensates and the effective algorithms for the numerical realisation of $n$-soliton solutions with large $n$.
{"title":"Riemann problem for polychromatic soliton gases: a testbed for the spectral kinetic theory","authors":"T. Congy, H. T. Carr, G. Roberti, G. A. El","doi":"arxiv-2405.05166","DOIUrl":"https://doi.org/arxiv-2405.05166","url":null,"abstract":"We use Riemann problem for soliton gas as a benchmark for a detailed\u0000numerical validation of the spectral kinetic theory for the Korteweg-de Vries\u0000(KdV) and the focusing nonlinear Schr\"odinger (fNLS) equations. We construct\u0000weak solutions to the kinetic equation for soliton gas describing collision of\u0000two dense \"polychromatic\" soliton gases composed of a finite number of\u0000\"monochromatic\" components, each consisting of solitons with nearly identical\u0000spectral parameters of the scattering operator in the Lax pair. The interaction\u0000between the gas components plays the key role in the emergent, large-scale\u0000hydrodynamic evolution. We then use the solutions of the spectral kinetic\u0000equation to evaluate macroscopic physical observables in KdV and fNLS soliton\u0000gases and compare them with the respective ensemble averages extracted from the\u0000\"exact\" soliton gas numerical solutions of the KdV and fNLS equations. To\u0000numerically synthesise dense polychromatic soliton gases we develop a new\u0000method which combines recent advances in the spectral theory of the so-called\u0000soliton condensates and the effective algorithms for the numerical realisation\u0000of $n$-soliton solutions with large $n$.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938070","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}
Alexander Dikopoltsev, Ina Heckelmann, Mathieu Bertrand, Mattias Beck, Giacomo Scalari, Oded Zilberberg, Jerome Faist
Photonic emulators have facilitated the investigation of numerous solid-state phenomena and have contributed to the development of optical devices inspired by quantum mechanics. Although current photonic emulators are constrained to bosonic behavior with local interactions, the utilization of active synthetic lattices holds promise for surpassing these limitations. In this study, we propose employing the modulated ring fast-gain laser as a foundation for emulating quench dynamics within a synthetic lattice that conforms to equal density filling of its reciprocal space. To illustrate the effectiveness of this emulation platform, we subject a dispersed Wannier-Stark ladder to quenching and directly observe oscillations, enabled by the fast-gain, along with their coherent stabilization to a single Wannier stark state. These coherent dynamics stem directly from our lasers liquid state of light, a characteristic resulting from fast-gain and explained by the rapid decay of fluctuations occurring on the system's shortest timescale. Additionally, by adequately biasing the lattice through detuning the modulation from the cavity resonance, this process supports oscillatory dynamics within the synthetic space.
{"title":"Quench dynamics of Wannier-Stark states in an active synthetic photonic lattice","authors":"Alexander Dikopoltsev, Ina Heckelmann, Mathieu Bertrand, Mattias Beck, Giacomo Scalari, Oded Zilberberg, Jerome Faist","doi":"arxiv-2405.04774","DOIUrl":"https://doi.org/arxiv-2405.04774","url":null,"abstract":"Photonic emulators have facilitated the investigation of numerous solid-state\u0000phenomena and have contributed to the development of optical devices inspired\u0000by quantum mechanics. Although current photonic emulators are constrained to\u0000bosonic behavior with local interactions, the utilization of active synthetic\u0000lattices holds promise for surpassing these limitations. In this study, we\u0000propose employing the modulated ring fast-gain laser as a foundation for\u0000emulating quench dynamics within a synthetic lattice that conforms to equal\u0000density filling of its reciprocal space. To illustrate the effectiveness of\u0000this emulation platform, we subject a dispersed Wannier-Stark ladder to\u0000quenching and directly observe oscillations, enabled by the fast-gain, along\u0000with their coherent stabilization to a single Wannier stark state. These\u0000coherent dynamics stem directly from our lasers liquid state of light, a\u0000characteristic resulting from fast-gain and explained by the rapid decay of\u0000fluctuations occurring on the system's shortest timescale. Additionally, by\u0000adequately biasing the lattice through detuning the modulation from the cavity\u0000resonance, this process supports oscillatory dynamics within the synthetic\u0000space.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938069","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}
K. Thulasidharan, N. Vishnu Priya, S. Monisha, M. Senthilvelan
We consider a hierarchy of nonlinear Schr"{o}dinger equations (NLSEs) and forecast the evolution of positon solutions using a deep learning approach called Physics Informed Neural Networks (PINN). Notably, the PINN algorithm accurately predicts positon solutions not only in the standard NLSE but also in other higher order versions, including cubic, quartic and quintic NLSEs. The PINN approach also effectively handles two coupled NLSEs and two coupled Hirota equations. In addition to the above, we report exact second-order positon solutions of the sextic NLSE and coupled generalized NLSE. These solutions are not available in the existing literature and we construct them through generalized Darboux transformation method. Further, we utilize PINNs to forecast their behaviour as well. To validate PINN's accuracy, we compare the predicted solutions with exact solutions obtained from analytical methods. The results show high fidelity and low mean squared error in the predictions generated by our PINN model.
{"title":"Predicting positon solutions of a family of Nonlinear Schrödinger equations through Deep Learning algorithm","authors":"K. Thulasidharan, N. Vishnu Priya, S. Monisha, M. Senthilvelan","doi":"arxiv-2405.04968","DOIUrl":"https://doi.org/arxiv-2405.04968","url":null,"abstract":"We consider a hierarchy of nonlinear Schr\"{o}dinger equations (NLSEs) and\u0000forecast the evolution of positon solutions using a deep learning approach\u0000called Physics Informed Neural Networks (PINN). Notably, the PINN algorithm\u0000accurately predicts positon solutions not only in the standard NLSE but also in\u0000other higher order versions, including cubic, quartic and quintic NLSEs. The\u0000PINN approach also effectively handles two coupled NLSEs and two coupled Hirota\u0000equations. In addition to the above, we report exact second-order positon\u0000solutions of the sextic NLSE and coupled generalized NLSE. These solutions are\u0000not available in the existing literature and we construct them through\u0000generalized Darboux transformation method. Further, we utilize PINNs to\u0000forecast their behaviour as well. To validate PINN's accuracy, we compare the\u0000predicted solutions with exact solutions obtained from analytical methods. The\u0000results show high fidelity and low mean squared error in the predictions\u0000generated by our PINN model.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"137 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938455","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}
Aitor Alaña, Michele Modugno, Pablo Capuzzi, D. M. Jezek
We analyze the pinning of vortices for a stationary rotating dipolar supersolid along the low-density paths between droplets as a function of the rotation frequency. We restrict ourselves to the stationary configurations of vortices with the same symmetry as that of the array of droplets. Our approach exploits the fact that the wave function of each droplet acquires a linear phase on the coordinates, and hence the relative phases between neighboring droplets allows us to predict the position of the vortices. For a confined system, the estimate accurately reproduces the Gross-Pitaevskii results in the spatial regions where the neighboring droplets are well defined.
{"title":"Phase-induced vortex pinning in rotating supersolid dipolar systems","authors":"Aitor Alaña, Michele Modugno, Pablo Capuzzi, D. M. Jezek","doi":"arxiv-2405.05099","DOIUrl":"https://doi.org/arxiv-2405.05099","url":null,"abstract":"We analyze the pinning of vortices for a stationary rotating dipolar\u0000supersolid along the low-density paths between droplets as a function of the\u0000rotation frequency. We restrict ourselves to the stationary configurations of\u0000vortices with the same symmetry as that of the array of droplets. Our approach\u0000exploits the fact that the wave function of each droplet acquires a linear\u0000phase on the coordinates, and hence the relative phases between neighboring\u0000droplets allows us to predict the position of the vortices. For a confined\u0000system, the estimate accurately reproduces the Gross-Pitaevskii results in the\u0000spatial regions where the neighboring droplets are well defined.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938457","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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