Vakhid A. Gani, Aliakbar Moradi Marjaneh
We study some properties of kink solutions of the model with non-polynomial potential obtained by deforming the well-known $φ^6$ field model. We consider the excitation spectrum of the kink. We also discuss the properties of the `kink+antikink' system as a whole that are not inherent to a solitary kink or antikink.
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We identify the kinks of a deformed O(3) linear Sigma model as the solutions of a set of first-order systems of equations; the above model is a generalization of the MSTB model with a three-component scalar field. Taking into account certain kink energy sum rules we show that the variety of kinks has the structure of a moduli space that can be compactified in a fairly natural way. The generic kinks, however, are unstable and Morse Theory provides the framework for the analysis of kink stability.
Dynamics of kink train solutions in deformed Multiple sine-Gordon models
研究薄非均匀层对 MsG 周期解及受扰 DsG 扭结链动力学的影响，利用相图分析其与缺陷作用时的稳定性、形变和演化。
We consider the scattering of kinks of the sinh-deformed $φ^4$ 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 …
It is shown how a integrable mechanical system provides all the localized static solutions of a deformation of the linear O(N)-sigma model in two space-time dimensions. The proof is based on the Hamilton-Jacobi separability of the mechanical analogue system that follows when time-independent field configurations are being considered. In particular, we describe the properties of the different kinds of kinks in such a way that a hierarchical structure of solitary wave manifolds emerges for distinct N.
The q-deformed kink of the $λϕ^4-$model is obtained via the normalisable ground state eigenfunction of a fluctuation operator associated with the q-deformed hyperbolic functions. From such a bosonic zero-mode the q-deformed potential in 1+1 dimensions is found, and we show that the q-deformed kink solution is a kink displaced away from the origin.
In this work we study kink-antikink and antikink-kink collisions in hyperbolic models of fourth and sixth order. We compared the patterns of scattering with known results from polynomial models of the same order. The hyperbolic models considered here tend to the polynomial $ϕ^4$ and $ϕ^6$ models in the limit of small values of the scalar field. We show that kinks and antikinks that interact hyperbolically with fourth order differ sensibly from those governed by the polynomial $ϕ^4$ model. The increasing of the order of interaction to the sixth order shows that the hyperbolic and polynomial mod…
Stability and decay of composite kinks/$Q$-balls solutions in a deformed $O(2N+1)$ linear sigma model
该论文解析求解了变形 $O(2N+1)$ 线性 sigma 模型在 $N=2$ 时的缺陷型解，分为简单解与复合解，并分析了其线性稳定性与衰变通道。
We compute the one-loop quantum corrections to the kink energies of the sinh-deformed $ϕ^{4}$ and $φ^{6}$ models in one space and one time dimensions. These models are constructed from the well-known polynomial $ϕ^{4}$ and $φ^{6}$ models by a deformation procedure. We also compute the vacuum polarization energy to the non-polynomial function $U(ϕ)=\frac{1}{4}(1-\sinh^{2}ϕ)^{2}$. This potential approaches the $ϕ^{4}$ model in the limit of small values of the scalar function. These energies are extracted from scattering data for fluctuations about the kink solutions. We show that for certain top…
We study kink-antikink collisions in a model which interpolates smoothly between the completely integrable sine-Gordon theory, the $ϕ^4$ model, and a $ϕ^6$-like model with three degenerate vacua. We find a rich variety of behaviours, including integrability breaking, resonance windows with increasingly irregular patterns, and new types of windows near the $ϕ^6$-like regime. False vacua, extra kink modes and kink fragmentation play important roles in the explanations of these phenomena. Our numerical studies are backed up by detailed analytical considerations.
Two hyperbolic-deformed field theoretic models are discussed. In both of them, due to the effect of specific deformation function on the well known $φ^4$ and $φ^6$ models, their internal structure may change significantly. Unlike the $φ^4$ kinks solutions, which has only one internal mode in addition to its translational mode, the kinks of the hyperbolic-deformed $φ^4$ model can have several internal modes. Moreover, the deformation on the $φ^6$ model has other interesting features, because the kinks of the $φ^6$ model have only a zero mode and the deformation may cause the appearance of inter…
We have studied the space-reflection symmetries of some soliton solutions of deformed sine-Gordon models in the context of the quasi-integrability concept. Considering a dual pair of anomalous Lax representations of the deformed model we compute analytically and numerically an infinite number of alternating conserved and asymptotically conserved charges through a modification of the usual techniques of integrable field theories. The charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e. kink-kink (odd parity) and kink-antikink (even parity) scatterings …
Deformed sine-Gordon (DSG) models $\partial_ξ\partial_η\, w + \frac{d}{dw}V(w) = 0$, with $V(w)$ being the deformed potential, are considered in the context of the Riccati-type pseudopotential approach. A compatibility condition of the deformed system of Riccati-type equations reproduces the equation of motion of the DSG models. Then, we provide a pair of linear systems of equations for DSG model, and provide an infinite tower of non-local conservation laws. Through a direct construction and supported by numerical simulations of soliton scatterings, we show that the DSG models, which have rece…
In this paper, we have studied the kink and antikink solutions in several neutral scalar models in 1+1 dimension. We follow the standard approach to write down the leading order and the second order force between long distance separated kink and antikink. The leading order force is proportional to exponential decay with respect to the distance between the two nearest kinks or antikinks. The second order force have a similar behavior with the larger decay factor, namely $3\over 2$. We make use of these properties to construct the kink lattice. The dynamics of the kink lattice with leading order…
Sine-Gordon deformed defects that exhibit unusual phenomenological features on the topological charge are investigated. The possibility of a smooth and continuous transition between topological (non null charge) and non-topological (null charge) scenarios of deformed defects supported by sine-Gordon structures is evinced by the analytical calculation of topological charges and localized energy distributions. By describing cyclic deformation chains, we show that a triggering sine-Gordon model simultaneously supports kink and lump-like defects, whose topological mass values are closed by trigono…
In this paper we investigate deformation of tachyon potentials and tachyon kink solutions. We consider the deformation of a DBI type action with gauge and tachyon fields living on D1-brane and D3-brane world-volume. We deform tachyon potentials to get other consistent tachyon potentials by using properly a deformation function depending on the gauge field components. Resolutions of singular tachyon kinks via deformation and applications of deformed tachyon potentials to scalar cosmology scenario are discussed.
In this work we investigate the issue of gravity and fermion localization and resonances in $(4,1)$-branes constructed with one scalar field coupled with gravity in deformed models. Such models give solutions for the scalar field that is the usual kink solution in the extra dimension for a parameter $p=1$ and deformations with a two-kink profile for odd $p>1$. Gravity is localized and resonant modes are found for small values of $p$. The coupling between the scalar field and spinors is a necessary condition for fermions to be localized on such branes. After performing a chiral decomposition of…
We consider a class of topological defects in $(1,1)$-dimensions with a deformed $ϕ^4$ kink structure whose stability analysis leads to a Schrödinger-like equation with a zero-mode and at least one vibrational (shape) mode. We are interested in the dynamics of kink-antikink collisions, focusing on the structure of two-bounce windows. For small deformation and for one or two vibrational modes, the observed two-bounce windows are explained by the standard mechanism of a resonant effect between the first vibrational and the translational modes. With the increasing of the deformation, the effect o…
We construct models of self-interacting scalar fields whose BPS solutions exhibit kink profiles which can be continuously deformed into two-kinks by varying one of the parameters of the self-interacting potential. The effective models are obtained from other models with two interacting scalar fields. The effective models are then applied in a brane-world scenario where we analyze the consequences of the thicker branes in the warped geometry and in the localization of gravity.
Large-$N$ Solution and Effective Action of "Twisted-Mass'' Deformed $\mathbb{CP}(N-1)$ Model
本文研究大$N$极限下由质量项形变的非超对称二维$\mathbb{CP}(N-1)$模型，发现其随质量变化发生强耦合与弱耦合Higgs相间的相变，并解决了先前研究的不稳定性问题。
Characteristic Modes of Non-minimally Coupled Thick Branes
本文研究非最小耦合厚膜的特征模式，分析两种厚膜模型的引力子零模局域性、共振KK模式及准正则模式，发现变形参数k增大可增加共振模式数量并延长第一共振寿命，低泛音QNF吻合良好。
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