Marcelo V. Flamarion, Efim Pelinovsky, Ekaterina Didenkulova
Algebraic soliton interactions with a periodic or quasi-periodic random force are investigated using the Benjamin-Ono equation. The random force is modeled as a Fourier series with a finite number of modes and random phases uniformly distributed, while its frequency spectrum has a Gaussian shape centered at a peak frequency. The expected value of the averaged soliton wave field is computed asymptotically and compared with numerical results, showing strong agreement. We identify parameter regimes where the averaged soliton field splits into two steady pulses and a regime where the soliton field splits into two solitons traveling in opposite directions. In the latter case, the averaged soliton speeds are variable. In both scenarios, the soliton field is damped by the external force. Additionally, we identify a regime where the averaged soliton exhibits the following behavior: it splits into two distinct solitons and then recombines to form a single soliton. This motion is periodic over time.
{"title":"Soliton dynamics in random fields: The Benjamin-Ono equation framework","authors":"Marcelo V. Flamarion, Efim Pelinovsky, Ekaterina Didenkulova","doi":"arxiv-2409.03790","DOIUrl":"https://doi.org/arxiv-2409.03790","url":null,"abstract":"Algebraic soliton interactions with a periodic or quasi-periodic random force\u0000are investigated using the Benjamin-Ono equation. The random force is modeled\u0000as a Fourier series with a finite number of modes and random phases uniformly\u0000distributed, while its frequency spectrum has a Gaussian shape centered at a\u0000peak frequency. The expected value of the averaged soliton wave field is\u0000computed asymptotically and compared with numerical results, showing strong\u0000agreement. We identify parameter regimes where the averaged soliton field\u0000splits into two steady pulses and a regime where the soliton field splits into\u0000two solitons traveling in opposite directions. In the latter case, the averaged\u0000soliton speeds are variable. In both scenarios, the soliton field is damped by\u0000the external force. Additionally, we identify a regime where the averaged\u0000soliton exhibits the following behavior: it splits into two distinct solitons\u0000and then recombines to form a single soliton. This motion is periodic over\u0000time.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217297","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 topical review we explore the dynamics of nonlinear lattices with a particular focus to Fermi-Pasta-Ulam-Tsingou type models that arise in the study of elastic media and, more specifically, granular crystals. We first revisit the workhorse of such lattices, namely traveling waves, both from a continuum, but also from a genuinely discrete perspective, both without and with a linear force component (induced by the so-called precompression). We then extend considerations to time-periodic states, examining dark breather structures in homogeneous crystals, as well as bright breathers in diatomic lattices. The last pattern that we consider extensively is the dispersive shock wave arising in the context of suitable Riemann (step) initial data. We show how the use of continuum (KdV) and discrete (Toda) integrable approximations can be used to get a first quantitative handle of the relevant waveforms. In all cases, theoretical analysis is accompanied by numerical computations and, where possible, by a recap and illustration of prototypical experimental results. We close the chapter by offering a number of ongoing and potential future directions and associated open problems in the field.
{"title":"Dynamics of Nonlinear Lattices","authors":"Christopher Chong, P. G. Kevrekidis","doi":"arxiv-2408.15837","DOIUrl":"https://doi.org/arxiv-2408.15837","url":null,"abstract":"In this topical review we explore the dynamics of nonlinear lattices with a\u0000particular focus to Fermi-Pasta-Ulam-Tsingou type models that arise in the\u0000study of elastic media and, more specifically, granular crystals. We first\u0000revisit the workhorse of such lattices, namely traveling waves, both from a\u0000continuum, but also from a genuinely discrete perspective, both without and\u0000with a linear force component (induced by the so-called precompression). We\u0000then extend considerations to time-periodic states, examining dark breather\u0000structures in homogeneous crystals, as well as bright breathers in diatomic\u0000lattices. The last pattern that we consider extensively is the dispersive shock\u0000wave arising in the context of suitable Riemann (step) initial data. We show\u0000how the use of continuum (KdV) and discrete (Toda) integrable approximations\u0000can be used to get a first quantitative handle of the relevant waveforms. In\u0000all cases, theoretical analysis is accompanied by numerical computations and,\u0000where possible, by a recap and illustration of prototypical experimental\u0000results. We close the chapter by offering a number of ongoing and potential\u0000future directions and associated open problems in the field.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217301","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 solve the fifth-order Korteweg-de Vries (fKdV) equation which is a modified KdV equation perturbed by a fifth-order derivative term multiplied by a small parameter $epsilon^2$, with $0< epsilon ll 1$. Unlike the KdV equation, the stationary fKdV equation does not exhibit exactly localized 1-soliton solution, instead it allows a solution which has a well defined central core similar to that of the KdV 1-soliton solution, accompanied by extremely small oscillatory standing wave tails on both sides of the core. The amplitude of the standing wave tail oscillations is $mathcal{O}(exp(-1/epsilon))$, i.e. it is beyond all orders small in perturbation theory. The analytical computation of the amplitude of these transcendentally small tail oscillations has been carried out up to $mathcal{O}(epsilon^5)$ order corrections by using the complex method of matched asymptotics. Also the long-standing discrepancy between the $mathcal{O}(epsilon^2)$ perturbative result of Grimshaw and Joshi (1995) and the numerical results of Boyd (1995) has been resolved. In addition to the stationary symmetric weakly localized solitary wave-like solutions, we analyzed the stationary asymmetric solutions of the fKdV equation which decay exponentially to zero on one side of the (slightly asymmetric) core and blows up to large negative values on other side of the core. The asymmetry is quantified by computing the third derivative of the solution at the origin which also turns out to be beyond all orders small in perturbation theory. The analytical computation of the third derivative of a function at the origin has also been carried out up to $mathcal{O}(epsilon^5)$ order corrections. We use the exponentially convergent pseudo-spectral method to solve the fKdV equation numerically. The analytical and the numerical results show remarkable agreement.
{"title":"Radiative tail of solitary waves in an extended Korteweg-de Vries equation","authors":"Muneeb Mushtaq","doi":"arxiv-2408.12356","DOIUrl":"https://doi.org/arxiv-2408.12356","url":null,"abstract":"We solve the fifth-order Korteweg-de Vries (fKdV) equation which is a\u0000modified KdV equation perturbed by a fifth-order derivative term multiplied by\u0000a small parameter $epsilon^2$, with $0< epsilon ll 1$. Unlike the KdV\u0000equation, the stationary fKdV equation does not exhibit exactly localized\u00001-soliton solution, instead it allows a solution which has a well defined\u0000central core similar to that of the KdV 1-soliton solution, accompanied by\u0000extremely small oscillatory standing wave tails on both sides of the core. The\u0000amplitude of the standing wave tail oscillations is\u0000$mathcal{O}(exp(-1/epsilon))$, i.e. it is beyond all orders small in\u0000perturbation theory. The analytical computation of the amplitude of these\u0000transcendentally small tail oscillations has been carried out up to\u0000$mathcal{O}(epsilon^5)$ order corrections by using the complex method of\u0000matched asymptotics. Also the long-standing discrepancy between the\u0000$mathcal{O}(epsilon^2)$ perturbative result of Grimshaw and Joshi (1995) and\u0000the numerical results of Boyd (1995) has been resolved. In addition to the\u0000stationary symmetric weakly localized solitary wave-like solutions, we analyzed\u0000the stationary asymmetric solutions of the fKdV equation which decay\u0000exponentially to zero on one side of the (slightly asymmetric) core and blows\u0000up to large negative values on other side of the core. The asymmetry is\u0000quantified by computing the third derivative of the solution at the origin\u0000which also turns out to be beyond all orders small in perturbation theory. The\u0000analytical computation of the third derivative of a function at the origin has\u0000also been carried out up to $mathcal{O}(epsilon^5)$ order corrections. We use\u0000the exponentially convergent pseudo-spectral method to solve the fKdV equation\u0000numerically. The analytical and the numerical results show remarkable\u0000agreement.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217299","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}
Nonlinear two-dimensional internal gravity waves (IGWs) in the atmospheres of the Earth and the Sun are studied. The resulting two-dimensional nonlinear equation has the form of a generalized nonlinear Schr"{o}dinger equation with nonlocal nonlinearity, that is when the nonlinear response depends on the wave intensity at some spatial domain. The modulation instability of IGWs is predicted, and specific cases for the Earth's atmosphere are considered. In a number of particular cases, the instability thresholds and instability growth rates are analytically found. Despite the nonlocal nonlinearity, we demonstrate the possibility of critical collapse of IGWs due to the scale homogeneity of the nonlinear term in spatial variables.
{"title":"Modulational instability and collapse of internal gravity waves in the atmosphere","authors":"Volodymyr M. Lashkin, Oleg K. Cheremnykh","doi":"arxiv-2408.12140","DOIUrl":"https://doi.org/arxiv-2408.12140","url":null,"abstract":"Nonlinear two-dimensional internal gravity waves (IGWs) in the atmospheres of\u0000the Earth and the Sun are studied. The resulting two-dimensional nonlinear\u0000equation has the form of a generalized nonlinear Schr\"{o}dinger equation with\u0000nonlocal nonlinearity, that is when the nonlinear response depends on the wave\u0000intensity at some spatial domain. The modulation instability of IGWs is\u0000predicted, and specific cases for the Earth's atmosphere are considered. In a\u0000number of particular cases, the instability thresholds and instability growth\u0000rates are analytically found. Despite the nonlocal nonlinearity, we demonstrate\u0000the possibility of critical collapse of IGWs due to the scale homogeneity of\u0000the nonlinear term in spatial variables.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"292 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217300","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}
Riki Dutta, Sagardeep Talukdar, Gautam K. Saharia, Sudipta Nandy
Davydova-Lashkin-Fokas-Lenells equation (DLFLE) is a gauged equivalent form of Fokas-Lenells equation (FLE) that addresses both spatio-temporal dispersion (STD) and nonlinear dispersion (ND) effects. The balance between those effects results a soliton which has always been an interesting topic in research due to its potential applicability as signal carrier in information technology. We have induced a variation to the dispersion effects and apply Hirota bilinear method to realise soliton solution of the proposed DLFLE and explore how the soliton dynamic behaves in accordance to the variation of the dispersion effects. The proposed equation is applicable for number of systems like ultrashort optical pulse, ioncyclotron plasma wave, Bose-Einstein condensate (BEC) matter-wave soliton under certain external fields, etc. The study on such systems under varying effects is very limited and we hope our work can benefit the researchers to understand soliton dynamics more and work on various other nonlinear fields under varying effects.
{"title":"Soliton Dynamics of a Gauged Fokas-Lenells Equation Under Varying Effects of Dispersion and Nonlinearity","authors":"Riki Dutta, Sagardeep Talukdar, Gautam K. Saharia, Sudipta Nandy","doi":"arxiv-2408.11533","DOIUrl":"https://doi.org/arxiv-2408.11533","url":null,"abstract":"Davydova-Lashkin-Fokas-Lenells equation (DLFLE) is a gauged equivalent form\u0000of Fokas-Lenells equation (FLE) that addresses both spatio-temporal dispersion\u0000(STD) and nonlinear dispersion (ND) effects. The balance between those effects\u0000results a soliton which has always been an interesting topic in research due to\u0000its potential applicability as signal carrier in information technology. We\u0000have induced a variation to the dispersion effects and apply Hirota bilinear\u0000method to realise soliton solution of the proposed DLFLE and explore how the\u0000soliton dynamic behaves in accordance to the variation of the dispersion\u0000effects. The proposed equation is applicable for number of systems like\u0000ultrashort optical pulse, ioncyclotron plasma wave, Bose-Einstein condensate\u0000(BEC) matter-wave soliton under certain external fields, etc. The study on such\u0000systems under varying effects is very limited and we hope our work can benefit\u0000the researchers to understand soliton dynamics more and work on various other\u0000nonlinear fields under varying effects.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"460 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227118","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 generation of second and third harmonics by an acoustic wave propagating along one dimension in a weakly nonlinear elastic medium that is loaded harmonically in time with frequency $omega_0$ at a single point in space, is analyzed by successive approximations starting with the linear case. It is noted that nonlinear waves have a speed of propagation that depends on their amplitude. It is also noted that both a free medium as well as a loaded medium generate higher harmonics, but that although the second harmonic of the free medium scales like the square of the linear wave, this is no longer the case when the medium is externally loaded. The shift in speed of propagation due to the nonlinearities is determined imposing that there be no resonant terms in a successive approximation solution scheme to the homogeneous problem. The result is then used to solve the inhomogeneous case also by successive approximations, up to the third order. At second order, the result is a second harmonic wave whose amplitude is modulated by a long wave, whose wavelength is inversely proportional to the shift in the speed of propagation of the linear wave due to nonlinearities. The amplitude of the long modulating wave scales like the amplitude of the linear wave to the four thirds. At short distances from the source a scaling proportional to the amplitude of the linear wave squared is recovered, as is a second harmonic amplitude that grows linearly with distance from the source and depends on the third-order elastic constant only. The third order solution is the sum of four amplitude-modulated waves, two of them oscillate with frequency $omega_0$ and the other two, third harmonics, with $3omega_0$. In each pair, one term scales like the amplitude of the linear wave to the five-thirds, and the other to the seven-thirds.
{"title":"Second and third harmonic generation of acoustic waves in a nonlinear elastic solid in one space dimension","authors":"Fernando Lund","doi":"arxiv-2408.11184","DOIUrl":"https://doi.org/arxiv-2408.11184","url":null,"abstract":"The generation of second and third harmonics by an acoustic wave propagating\u0000along one dimension in a weakly nonlinear elastic medium that is loaded\u0000harmonically in time with frequency $omega_0$ at a single point in space, is\u0000analyzed by successive approximations starting with the linear case. It is\u0000noted that nonlinear waves have a speed of propagation that depends on their\u0000amplitude. It is also noted that both a free medium as well as a loaded medium\u0000generate higher harmonics, but that although the second harmonic of the free\u0000medium scales like the square of the linear wave, this is no longer the case\u0000when the medium is externally loaded. The shift in speed of propagation due to\u0000the nonlinearities is determined imposing that there be no resonant terms in a\u0000successive approximation solution scheme to the homogeneous problem. The result\u0000is then used to solve the inhomogeneous case also by successive approximations,\u0000up to the third order. At second order, the result is a second harmonic wave\u0000whose amplitude is modulated by a long wave, whose wavelength is inversely\u0000proportional to the shift in the speed of propagation of the linear wave due to\u0000nonlinearities. The amplitude of the long modulating wave scales like the\u0000amplitude of the linear wave to the four thirds. At short distances from the\u0000source a scaling proportional to the amplitude of the linear wave squared is\u0000recovered, as is a second harmonic amplitude that grows linearly with distance\u0000from the source and depends on the third-order elastic constant only. The third\u0000order solution is the sum of four amplitude-modulated waves, two of them\u0000oscillate with frequency $omega_0$ and the other two, third harmonics, with\u0000$3omega_0$. In each pair, one term scales like the amplitude of the linear\u0000wave to the five-thirds, and the other to the seven-thirds.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217318","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 cubic nonlinear Schrodinger equation (NLS) in one dimension is considered in the presence of an intensity-dependent dispersion term. We study bright solitary waves with smooth profiles which extend from the limit where the dependence of the dispersion coefficient on the wave intensity is negligible to the limit where the solitary wave becomes singular due to vanishing dispersion coefficient. We analyze and numerically explore the stability for such smooth solitary waves, showing with the help of numerical approximations that the family of solitary waves becomes unstable in the intermediate region between the two limits, while being stable in both limits. This bistability, that has also been observed in other NLS equations with the generalized nonlinearity, brings about interesting dynamical transitions from one stable branch to another stable branch, that are explored in direct numerical simulations of the NLS equation with the intensity-dependent dispersion term.
{"title":"Stability of smooth solitary waves under intensity--dependent dispersion","authors":"P. G. Kevrekidis, D. E. Pelinovsky, R. M. Ross","doi":"arxiv-2408.11192","DOIUrl":"https://doi.org/arxiv-2408.11192","url":null,"abstract":"The cubic nonlinear Schrodinger equation (NLS) in one dimension is considered\u0000in the presence of an intensity-dependent dispersion term. We study bright\u0000solitary waves with smooth profiles which extend from the limit where the\u0000dependence of the dispersion coefficient on the wave intensity is negligible to\u0000the limit where the solitary wave becomes singular due to vanishing dispersion\u0000coefficient. We analyze and numerically explore the stability for such smooth\u0000solitary waves, showing with the help of numerical approximations that the\u0000family of solitary waves becomes unstable in the intermediate region between\u0000the two limits, while being stable in both limits. This bistability, that has\u0000also been observed in other NLS equations with the generalized nonlinearity,\u0000brings about interesting dynamical transitions from one stable branch to\u0000another stable branch, that are explored in direct numerical simulations of the\u0000NLS equation with the intensity-dependent dispersion term.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217316","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 study quantum droplets emerging in a quasi-one-dimensional asymmetric mixture of two atomic species with different intra-component coupling constants. We find that such mixtures support a rich variety of multipole quantum droplets, where the macroscopic wavefunction of one component changes its sign and features distinctive multipole structure, while the wavefunction of another component does not have zeros. Such multipole droplets have no counterparts in the reduced single-component model frequently used to describe symmetric one-dimensional mixtures. We study transformations of multipole states upon variation of the chemical potential of each component and demonstrate that quantum droplets can split into separated fundamental states, transform into flat-top multipoles, or into multipole component coupled to flat-top state with several humps on it, akin to anti-dark solitons. Multipole quantum droplets described here are stable in large part of their existence domain. Our findings essentially broaden the family of quantum droplet states emerging in the beyond-meanfield regime and open the way for observation of such heterostructured states in Bose-Bose mixtures.
{"title":"Multipole quantum droplets in quasi-one-dimensional asymmetric mixtures","authors":"Yaroslav V. Kartashov, Dmitry A. Zezyulin","doi":"arxiv-2408.09979","DOIUrl":"https://doi.org/arxiv-2408.09979","url":null,"abstract":"We study quantum droplets emerging in a quasi-one-dimensional asymmetric\u0000mixture of two atomic species with different intra-component coupling\u0000constants. We find that such mixtures support a rich variety of multipole\u0000quantum droplets, where the macroscopic wavefunction of one component changes\u0000its sign and features distinctive multipole structure, while the wavefunction\u0000of another component does not have zeros. Such multipole droplets have no\u0000counterparts in the reduced single-component model frequently used to describe\u0000symmetric one-dimensional mixtures. We study transformations of multipole\u0000states upon variation of the chemical potential of each component and\u0000demonstrate that quantum droplets can split into separated fundamental states,\u0000transform into flat-top multipoles, or into multipole component coupled to\u0000flat-top state with several humps on it, akin to anti-dark solitons. Multipole\u0000quantum droplets described here are stable in large part of their existence\u0000domain. Our findings essentially broaden the family of quantum droplet states\u0000emerging in the beyond-meanfield regime and open the way for observation of\u0000such heterostructured states in Bose-Bose mixtures.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217319","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 control over the geometry and topology of quantum systems is crucial for advancing novel quantum technologies. This work provides a synthesis of recent insights into the behaviour of quantum vortices within atomic Bose-Einstein condensates (BECs) subject to curved geometric constraints. We highlight the significant impact of the curvature on the condensate density and phase distribution, particularly in quasi-one-dimensional waveguides for different angular momentum states. An engineered periodic transport of the quantized vorticity between density-coupled ring-shaped condensates is discussed. The significant role of curved geometry in shaping the dynamics of rotational Josephson vortices in long atomic Josephson junctions is illustrated for the system of vertically stacked toroidal condensates. Different methods for the controlled creation of rotational Josephson vortices in coupled ring systems are described in the context of the formation of long-lived vortex configurations in shell-shaped BECs with cylindrical geometry. Future directions of explorations of vortices in curved geometries with implications for quantum information processing and sensing technologies are discussed.
{"title":"Quantum Vortices in Curved Geometries","authors":"A. Tononi, L. Salasnich, A. Yakimenko","doi":"arxiv-2408.09270","DOIUrl":"https://doi.org/arxiv-2408.09270","url":null,"abstract":"The control over the geometry and topology of quantum systems is crucial for\u0000advancing novel quantum technologies. This work provides a synthesis of recent\u0000insights into the behaviour of quantum vortices within atomic Bose-Einstein\u0000condensates (BECs) subject to curved geometric constraints. We highlight the\u0000significant impact of the curvature on the condensate density and phase\u0000distribution, particularly in quasi-one-dimensional waveguides for different\u0000angular momentum states. An engineered periodic transport of the quantized\u0000vorticity between density-coupled ring-shaped condensates is discussed. The\u0000significant role of curved geometry in shaping the dynamics of rotational\u0000Josephson vortices in long atomic Josephson junctions is illustrated for the\u0000system of vertically stacked toroidal condensates. Different methods for the\u0000controlled creation of rotational Josephson vortices in coupled ring systems\u0000are described in the context of the formation of long-lived vortex\u0000configurations in shell-shaped BECs with cylindrical geometry. Future\u0000directions of explorations of vortices in curved geometries with implications\u0000for quantum information processing and sensing technologies are discussed.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217320","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 present an exact solution to the problem of a self-consistent equilibrium force-free magnetic flux rope. Unlike other approaches, we use magnetostatic equations and assume only a relatively rapid decrease in the axial magnetic field at infinity. For the first time we obtain a new nonlinear equation for the axial current density, the derivation of which does not require any phenomenological assumptions. From the resulting nonlinear equation, we analytically find the radial profiles of the components of the magnetic field strength and current density.
{"title":"Self-consistent equilibrium of a force-free magnetic flux rope","authors":"O. K. Cheremnykh, V. M. Lashkin","doi":"arxiv-2408.08512","DOIUrl":"https://doi.org/arxiv-2408.08512","url":null,"abstract":"We present an exact solution to the problem of a self-consistent equilibrium\u0000force-free magnetic flux rope. Unlike other approaches, we use magnetostatic\u0000equations and assume only a relatively rapid decrease in the axial magnetic\u0000field at infinity. For the first time we obtain a new nonlinear equation for\u0000the axial current density, the derivation of which does not require any\u0000phenomenological assumptions. From the resulting nonlinear equation, we\u0000analytically find the radial profiles of the components of the magnetic field\u0000strength and current density.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217321","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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