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Ciurla D, Forgács P, Lukács Á, Romańczukiewicz T. Negative radiation pressure in Bose-Einstein condensates. Phys Rev E 2024; 109:014228. [PMID: 38366411 DOI: 10.1103/physreve.109.014228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 01/02/2024] [Indexed: 02/18/2024]
Abstract
In two-component nonlinear Schrödinger equations, the force exerted by incident monochromatic plane waves on an embedded dark soliton and on dark-bright-type solitons is investigated, both perturbatively and by numerical simulations. When the incoming wave is nonvanishing only in the orthogonal component to that of the embedded dark soliton, its acceleration is in the opposite direction to that of the incoming wave. This somewhat surprising phenomenon can be attributed to the well-known negative effective mass of the dark soliton. When a dark-bright soliton, whose effective mass is also negative, is hit by an incoming wave nonvanishing in the component corresponding to the dark soliton, the direction of its acceleration coincides with that of the incoming wave. This implies that the net force acting on it is in the opposite direction to that of the incoming wave. This rather counterintuitive effect is a yet another manifestation of negative radiation pressure exerted by the incident wave, observed in other systems. When a dark-bright soliton interacts with an incoming wave in the component of the bright soliton, it accelerates in the opposite direction; hence the force is pushing it now. We expect that these remarkable effects, in particular the negative radiation pressure, can be experimentally verified in Bose-Einstein condensates.
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Affiliation(s)
- Dominik Ciurla
- Institute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Péter Forgács
- Wigner RCP RMI, POB 49, 1525 Budapest, Hungary
- Institut Denis-Poisson, UMR No. 7013, CNRS, Université de Tours, Parc de Grandmont, 37200 Tours, France
| | - Árpád Lukács
- Wigner RCP RMI, POB 49, 1525 Budapest, Hungary
- Department of Mathematical Sciences, Durham University, Stockton Road, Durham DH1 3LE, United Kingdom
| | - Tomasz Romańczukiewicz
- Institute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland
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2
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Qin YH, Zhao LC, Ling L. Nondegenerate bound-state solitons in multicomponent Bose-Einstein condensates. Phys Rev E 2019; 100:022212. [PMID: 31574652 DOI: 10.1103/physreve.100.022212] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2019] [Indexed: 06/10/2023]
Abstract
We investigate nondegenerate bound-state solitons systematically in multicomponent Bose-Einstein condensates, through developing the Darboux transformation method to derive exact soliton solutions analytically. In particular, we show that bright solitons with nodes correspond to the excited bound states in effective quantum wells, in sharp contrast to the bright solitons and dark solitons reported before (which usually correspond to ground state and free state, respectively). We further demonstrate that bound-state solitons with nodes are induced by incoherent superposition of solitons in different components. Moreover, we reveal that the interactions between these bound-state solitons are usually inelastic, caused by the incoherent interactions between solitons in different components and the coherent interactions between solitons in the same component. Additionally, the detailed spectral stability analysis demonstrates the stability of nondegenerate bound-state solitons. The bound-state solitons can be used to study many different physical problems, such as beating dynamics, spin-orbit coupling effects, quantum fluctuations, and even quantum entanglement states.
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Affiliation(s)
- Yan-Hong Qin
- School of Physics, Northwest University, Xi'an 710127, China
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
| | - Li-Chen Zhao
- School of Physics, Northwest University, Xi'an 710127, China
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
| | - Liming Ling
- School of Mathematics, South China University of Technology, Guangzhou 510640, China
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3
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Contento L, Mimura M. Complex pattern formation driven by the interaction of stable fronts in a competition-diffusion system. J Math Biol 2019; 80:303-342. [DOI: 10.1007/s00285-019-01370-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2018] [Revised: 03/22/2019] [Indexed: 12/01/2022]
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Haim L, Hagberg A, Meron E. Non-monotonic resonance in a spatially forced Lengyel-Epstein model. CHAOS (WOODBURY, N.Y.) 2015; 25:064307. [PMID: 26117118 DOI: 10.1063/1.4921768] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We study resonant spatially periodic solutions of the Lengyel-Epstein model modified to describe the chlorine dioxide-iodine-malonic acid reaction under spatially periodic illumination. Using multiple-scale analysis and numerical simulations, we obtain the stability ranges of 2:1 resonant solutions, i.e., solutions with wavenumbers that are exactly half of the forcing wavenumber. We show that the width of resonant wavenumber response is a non-monotonic function of the forcing strength, and diminishes to zero at sufficiently strong forcing. We further show that strong forcing may result in a π/2 phase shift of the resonant solutions, and argue that the nonequilibrium Ising-Bloch front bifurcation can be reversed. We attribute these behaviors to an inherent property of forcing by periodic illumination, namely, the increase of the mean spatial illumination as the forcing amplitude is increased.
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Affiliation(s)
- Lev Haim
- Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| | - Aric Hagberg
- Center for Nonlinear Studies, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Ehud Meron
- Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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Gomila D, Colet P, Walgraef D. Theory for the spatiotemporal dynamics of domain walls close to a nonequilibrium Ising-Bloch transition. PHYSICAL REVIEW LETTERS 2015; 114:084101. [PMID: 25768763 DOI: 10.1103/physrevlett.114.084101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2014] [Indexed: 06/04/2023]
Abstract
We derive a generic model for the interaction of domain walls close to a nonequilibrium-Bloch transition. The universal scenario predicted by the model includes stationary Ising and Bloch localized structures (dissipative solitons), as well as drifting and oscillating Bloch structures. Our theory also explains the behavior of Bloch walls during a collision. The results are confirmed by numerical simulations of the Ginzburg-Landau equation forced at twice its natural frequency and are in agreement with previous observations in several physical systems.
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Affiliation(s)
- Damià Gomila
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain
| | - Pere Colet
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain
| | - Daniel Walgraef
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain
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6
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Haim L, Mau Y, Meron E. Spatial forcing of pattern-forming systems that lack inversion symmetry. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022904. [PMID: 25215796 DOI: 10.1103/physreve.90.022904] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2014] [Indexed: 06/03/2023]
Abstract
The entrainment of periodic patterns to spatially periodic parametric forcing is studied. Using a weak nonlinear analysis of a simple pattern formation model we study the resonant responses of one-dimensional systems that lack inversion symmetry. Focusing on the first three n:1 resonances, in which the system adjusts its wavenumber to one nth of the forcing wavenumber, we delineate commonalities and differences among the resonances. Surprisingly, we find that all resonances show multiplicity of stable phase states, including the 1:1 resonance. The phase states in the 2:1 and 3:1 resonances, however, differ from those in the 1:1 resonance in remaining symmetric even when the inversion symmetry is broken. This is because of the existence of a discrete translation symmetry in the forced system. As a consequence, the 2:1 and 3:1 resonances show stationary phase fronts and patterns, whereas phase fronts within the 1:1 resonance are propagating and phase patterns are transients. In addition, we find substantial differences between the 2:1 resonance and the other two resonances. While the pattern forming instability in the 2:1 resonance is supercritical, in the 1:1 and 3:1 resonances it is subcritical, and while the inversion asymmetry extends the ranges of resonant solutions in the 1:1 and 3:1 resonances, it has no effect on the 2:1 resonance range. We conclude by discussing a few open questions.
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Affiliation(s)
- Lev Haim
- Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel and Department of Oncology, Soroka University Medical Center, Beer Sheva, 84101, Israel
| | - Yair Mau
- Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel and Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina 27708, USA
| | - Ehud Meron
- Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel and Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990, Israel
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Janutka A. Externally driven transmission and collisions of domain walls in ferromagnetic wires. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056607. [PMID: 21728682 DOI: 10.1103/physreve.83.056607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2010] [Revised: 01/16/2011] [Indexed: 05/31/2023]
Abstract
Analytical multidomain solutions to the dynamical (Landau-Lifshitz-Gilbert) equation of a one-dimensional ferromagnet including an external magnetic field and spin-polarized electric current are found using the Hirota bilinearization method. A standard approach to solve the Landau-Lifshitz equation (without the Gilbert term) is modified in order to treat the dissipative dynamics. I establish the relations between the spin interaction parameters (the constants of exchange, anisotropy, dissipation, external-field intensity, and electric-current intensity) and the domain-wall parameters (width and velocity) and compare them to the results of the Walker approximation and micromagnetic simulations. The domain-wall motion driven by a longitudinal external field is analyzed with especial relevance to the field-induced collision of two domain walls. I determine the result of such a collision (which is found to be an elastic one) on the domain-wall parameters below and above the Walker breakdown (in weak- and strong-field regimes). Single-domain-wall dynamics in the presence of an external transverse field is studied with relevance to the challenge of increasing the domain-wall velocity below the breakdown.
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Affiliation(s)
- Andrzej Janutka
- Institute of Physics, Wroclaw University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
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Janutka A. Externally driven collisions of domain walls in bistable systems near criticality. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056608. [PMID: 21728683 DOI: 10.1103/physreve.83.056608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2010] [Revised: 02/13/2011] [Indexed: 05/31/2023]
Abstract
Multidomain solutions to the time-dependent Ginzburg-Landau equation in the presence of an external field are analyzed using the Hirota bilinearization method. Domain-wall collisions are studied in detail considering different regimes of the critical parameter. I show the dynamics of the Ising and Bloch domain walls of the Ginzburg-Landau equation in the bistable regime to be similar to that of the Landau-Lifshitz domain walls. Domain-wall reflections lead to the appearance of bubble and pattern structures. Above the Bloch-Ising transition point, spatial structures are determined by the collisions of fronts propagating into an unstable state. Mutual annihilation of such fronts is described.
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Affiliation(s)
- Andrzej Janutka
- Institute of Physics, Wroclaw University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
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Barashenkov IV, Zemlyanaya EV. Soliton complexity in the damped-driven nonlinear Schrödinger equation: stationary to periodic to quasiperiodic complexes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056610. [PMID: 21728685 DOI: 10.1103/physreve.83.056610] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2010] [Revised: 02/07/2011] [Indexed: 05/31/2023]
Abstract
Stationary and oscillatory bound states, or complexes, of the damped-driven solitons are numerically path-followed in the parameter space. We compile a chart of the two-soliton attractors, complementing the one-soliton attractor chart.
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Affiliation(s)
- I V Barashenkov
- Department of Mathematics, University of Cape Town, Rondebosch 7701, South Africa.
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Syafwan M, Susanto H, Cox SM. Discrete solitons in electromechanical resonators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:026207. [PMID: 20365638 DOI: 10.1103/physreve.81.026207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2009] [Indexed: 05/29/2023]
Abstract
We consider a particular type of parametrically driven discrete Klein-Gordon system describing microdevices and nanodevices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear Schrödinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright and dark discrete solitons admitted by the Klein-Gordon system through the discrete Schrödinger equation. We show that a parametric driving can not only destabilize onsite bright solitons, but also stabilize intersite bright discrete solitons and onsite and intersite dark solitons. Most importantly, we show that there is a range of values of the driving coefficient for which dark solitons are stable, for any value of the coupling constant, i.e., oscillatory instabilities are totally suppressed. Stability windows of all the fundamental solitons are presented and approximations to the onset of instability are derived using perturbation theory, with accompanying numerical results. Numerical integrations of the Klein-Gordon equation are performed, confirming the relevance of our analysis.
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Affiliation(s)
- M Syafwan
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
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11
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Gaididei YB, Christiansen PL. Ising and Bloch domain walls in a two-dimensional parametrically driven Ginzburg-Landau equation model with nonlinearity management. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:026610. [PMID: 18850965 DOI: 10.1103/physreve.78.026610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2008] [Indexed: 05/26/2023]
Abstract
We study a parametrically driven Ginzburg-Landau equation model with nonlinear management. The system is made of laterally coupled long active waveguides placed along a circumference. Stationary solutions of three kinds are found: periodic Ising states and two types of Bloch states, staggered and unstaggered. The stability of these states is investigated analytically and numerically. The nonlinear dynamics of the Bloch states are described by a complex Ginzburg-Landau equation with linear and nonlinear parametric driving. The switching between the staggered and unstaggered Bloch states under the action of direct ac forces is shown.
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Affiliation(s)
- Yu B Gaididei
- Bogolyubov Institute for Theoretical Physics, Metrologichna Street 14 B, 03680, Kiev, Ukraine
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12
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Barashenkov IV, Woodford SR, Zemlyanaya EV. Interactions of parametrically driven dark solitons. I. Néel-Néel and Bloch-Bloch interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:026604. [PMID: 17358433 DOI: 10.1103/physreve.75.026604] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2005] [Revised: 11/03/2006] [Indexed: 05/14/2023]
Abstract
We study interactions between the dark solitons of the parametrically driven nonlinear Schrödinger equation, Eq. 1 . When the driving strength, h , is below sqrt[gamma(2)+1/9], two well-separated Néel walls may repel or attract. They repel if their initial separation 2z(0) is larger than the distance 2zu between the constituents in the unstable stationary complex of two walls. They attract and annihilate if 2z(0) is smaller than 2zu. Two Néel walls with h lying between sqrt[gamma(2)+1/9] and a threshold driving strength hsn attract for 2z(0)<2zu and evolve into a stable stationary bound state for 2z(0)>2zu. Finally, the Néel walls with h greater than hsn attract and annihilate-irrespective of their initial separation. Two Bloch walls of opposite chiralities attract, while Bloch walls of like chiralities repel-except near the critical driving strength, where the difference between the like-handed and oppositely handed walls becomes negligible. In this limit, similarly handed walls at large separations repel while those placed at shorter distances may start moving in the same direction or transmute into an oppositely handed pair and attract. The collision of two Bloch walls or two nondissipative Néel walls typically produces a quiescent or moving breather.
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Affiliation(s)
- I V Barashenkov
- Department of Physics, University of Bayreuth, D-95440 Bayreuth, Germany.
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Barashenkov IV, Woodford SR. Interactions of parametrically driven dark solitons. II. Néel-Bloch interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:026605. [PMID: 17358434 DOI: 10.1103/physreve.75.026605] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2006] [Indexed: 05/14/2023]
Abstract
The interaction between a Bloch and a Néel wall in the parametrically driven nonlinear Schrödinger equation is studied by following the dissociation of their unstable bound state. Mathematically, the analysis focuses on the splitting of a fourfold zero eigenvalue associated with a pair of infinitely separated Bloch and Néel walls. It is shown that a Bloch and a Néel wall interact as two classical particles, one with positive and the other one with negative mass.
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Affiliation(s)
- I V Barashenkov
- Department of Physics, University of Bayreuth, D-95440 Bayreuth, Germany.
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Wang H, Zhang K, Ouyang Q. Resonant-pattern formation induced by additive noise in periodically forced reaction-diffusion systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:036210. [PMID: 17025732 DOI: 10.1103/physreve.74.036210] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2006] [Revised: 08/16/2006] [Indexed: 05/12/2023]
Abstract
We report frequency-locked resonant patterns induced by additive noise in periodically forced reaction-diffusion Brusselator model. In the regime of 2:1 frequency-locking and homogeneous oscillation, the introduction of additive noise, which is colored in time and white in space, generates and sustains resonant patterns of hexagons, stripes, and labyrinths which oscillate at half of the forcing frequency. Both the noise strength and the correlation time control the pattern formation. The system transits from homogeneous to hexagons, stripes, and to labyrinths successively as the noise strength is adjusted. Good frequency-locked patterns are only sustained by the colored noise and a finite time correlation is necessary. At the limit of white noise with zero temporal correlation, irregular patterns which are only nearly resonant come out as the noise strength is adjusted. The phenomenon induced by colored noise in the forced reaction-diffusion system is demonstrated to correspond to noise-induced Turing instability in the corresponding forced complex Ginzburg-Landau equation.
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Affiliation(s)
- Hongli Wang
- Department of Physics, Peking University, Beijing 100871, People's Republic of China
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Reznik GM, Zeitlin V. Resonant excitation of rossby waves in the equatorial waveguide and their nonlinear evolution. PHYSICAL REVIEW LETTERS 2006; 96:034502. [PMID: 16486711 DOI: 10.1103/physrevlett.96.034502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2005] [Indexed: 05/06/2023]
Abstract
Nonlinear interactions between the baroclinic Rossby waves trapped in the equatorial waveguide and the barotropic Rossby waves freely propagating across the equator are studied within the two-layer model of the atmosphere, or the ocean. It is shown that a barotropic wave can resonantly excite a pair of baroclinic waves with amplitudes much greater than its proper amplitude. The envelopes of the baroclinic waves obey Ginzburg-Landau-type equations and exhibit nonlinear saturation and formation of characteristic "domain-wall" and "dark-soliton" defects.
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Affiliation(s)
- G M Reznik
- P.P. Shirshov Institute of Oceanology, Moscow, Russia
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