Topological defects with power-law tails

Radomskiy, Roman V.; Mrozovskaya, Elizaveta V.; Gani, Vakhid A.; Christov, Ivan

doi:10.1088/1742-6596/798/1/012087

Cited by 34 publications

(48 citation statements)

References 18 publications

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“…Field-theoretic models with polynomial potentials that can exhibit topological solutions (kinks) are also important in cosmological applications of been studied systematically. Nevertheless, the work has been started [8,10,[32][33][34][35][36][37][38][39]. In particular, exact (but implicit) solutions for the kink shapes of various ϕ 8 , ϕ 10 and ϕ 12 field theories have been obtained [8], the excitation spectra of the ϕ 8 kinks have been studied, resonance phenomena in the kink-antikink scattering have been found, and their relation to the kinks' vibrational excitations has been discussed [35,36,38,39].…”

Section: Introductionmentioning

confidence: 99%

Long-range interactions of kinks

et al. 2019

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We present a computational analysis of the long-range interactions of solitary waves in higherorder field theories. Our vehicle of choice is the ϕ 8 field theory, although we explore similar issues in example ϕ 10 and ϕ 12 models. In particular, we discuss the fundamental differences between the latter higher-order models and the standard ϕ 4 model. Upon establishing the power-law asymptotics of the model's solutions' approach towards one of the steady states, we make the case that such asymptotics require particular care in setting up multi-soliton initial conditions. A naive implementation of additive or multiplicative ansätze gives rise to highly pronounced radiation effects and eventually leads to the illusion of a repulsive interaction between a kink and an antikink in such higher-order field theories. We propose and compare several methods for how to "distill" the initial data into suitable ansätze, and we show how these approaches capture the attractive nature of interactions between the topological solitons in the presence of power-law tails (longrange interactions). This development paves the way for a systematic examination of solitary wave interactions in higher-order field theories and raises some intriguing questions regarding potential experimental observations of such interactions. As an Appendix, we present an analysis of kinkantikink interactions in the example models via the method of collective coordinates.the Higgs field [13,14]. Beyond field theoretic models with polynomial potentials, finitegap potentials of Lamé type also lead to scalar field theories with exotic kink solutions, now relevant in the context of sypersymmetric quantum mechanics [15,16] and extended to PT -symmetric situations [17].Although the above-mentioned models with polynomial potentials are non-integrable, studying their properties in (1+1)-dimensional space-time is of common interest because, in this setting, a variety of analytical (and numerical) methods can be straightforwardly deployed to fully understand the dynamics of coherent structures. Moreover, (1+1)dimensional solutions may be relevant to more realistic situations in higher dimensions; for example, the equations for certain five-dimensional brane-world phenomenologies can be reduced to differential equations similar to those of (1+1)-dimensional field theories [18].Such models with polynomial potentials of even degree allow kinks -topological solutions that interpolate between neighboring minima of the potential, i.e. vacua of the model [19].Properties of kinks of the ϕ 4 and ϕ 6 models are well-studied, yielding many important results [4,7,[20][21][22][23][24][25][26][27][28][29][30][31]. At the same time, polynomial potentials of higher degrees have not

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Section: Introductionmentioning

confidence: 99%

Long-range interactions of kinks

et al. 2019

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“…A broad class of (1, 1)-dimensional models with polynomial potentials such as the ϕ 4 , ϕ 6 , ϕ 8 models, and those with higher degree polynomial self-interaction has been considered [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76]. One should also mention the new results on the long-range interaction between kinks [74][75][76][77][78][79]. Other models with non-polynomial potentials are also being discussed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model

2018

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We consider the scattering of kinks of the sinhdeformed ϕ 4 model, which is obtained from the well-known ϕ 4 model by means of the deformation procedure. Depending on the initial velocity v in of the colliding kinks, different collision scenarios are realized. There is a critical value v cr of the initial velocity, which separates the regime of reflection (at v in > v cr ) and that of a complicated interaction (at v in < v cr ) with kinks' capture and escape windows. Besides that, at v in below v cr we observe the formation of a bound state of two oscillons, as well as their escape at some values of v in .

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“…The interactions of kinks (and antikinks) are studied using different methods, in particular, quasi-exact methods such as the numerical solution of the equations of motion, which are partial differential equations, and approximate methods such as the collective coordinate approximation [27,[41][42][43][44][45][46] and the Manton's method [47][48][49]. The simple collective…”

Section: Introductionmentioning

confidence: 99%

Multi-kink collisions in the ϕ 6 model

Marjaneh

Gani

Saadatmand

et al. 2017

J. High Energ. Phys.

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We study simultaneous collisions of two, three, and four kinks and antikinks of the φ 6 model at the same spatial point. Unlike the φ 4 kinks, the φ 6 kinks are asymmetric and this enriches the variety of the collision scenarios. In our numerical simulations we observe both reflection and bound state formation depending on the number of kinks and on their spatial ordering in the initial configuration. We also analyze the extreme values of the energy densities and the field gradient observed during the collisions. Our results suggest that very high energy densities can be produced in multi-kink collisions in a controllable manner. Appearance of high energy density spots in multi-kink collisions can be important in various physical applications of the Klein-Gordon model.

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Topological defects with power-law tails

Cited by 34 publications

References 18 publications

Long-range interactions of kinks

Long-range interactions of kinks

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model

Multi-kink collisions in the ϕ 6 model

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