arXiv subjects

Vakhid A. Gani

Publications and source records attributed to Vakhid A. Gani.

At least 37 records · Page 2Linked to original sources

arXiv2020

Kinks in the relativistic model with logarithmic nonlinearity

We study the properties of a relativistic model with logarithmic nonlinearity. We show that such model allows two types of solutions: topologically trivial (gaussons) and topologically non-trivial (kinks), depending on a sign of the nonlinear coupling. We focus primarily on the kinks' case and study their scattering properties. For the kink-antikink scattering, we have found a critical value of the initial velocity, which separates two different scenarios of scattering. For the initial velocities below this critical value, the kinks form a bound state, which then decays slowly. If the initial velocities are above the critical value, the kinks collide, bounce and eventually escape to infinities. During this process, the higher initial velocity is, the greater is the elasticity of the collision. We also study excitation spectrum of the kink solution.

hep-th↗

arXiv2019

Multi-kink scattering in the double sine-Gordon model

We study collisions of two, three, and four kinks of the double sine-Gordon model. The initial conditions are taken in a special form in order to provide collision of all kinks in one point. We obtain dependences of the maximal energy densities on the model parameter. We also analyze the final states observed in these collisions.

hep-th↗

arXiv2019

Kink-kink and kink-antikink interactions with long-range tails

In this Letter, we address the {long-range interaction} between kinks and antikinks, as well as kinks and kinks, in $φ^{2n+4}$ field theories for $n>1$. The kink-antikink interaction is generically attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the $(\frac{2n}{n-1})$th power of their separation, and we identify the general prefactor for {\it arbitrary} $n$. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory and numerics for the cases of $n=2$ ($φ^8$ model), $n=3$ ($φ^{10}$ model) and $n=4$ ($φ^{12}$ model).

hep-th↗

arXiv2019

Superheavy objects composed of nuclear and dark matter

We consider a model of $O$He atomic dark matter formed by Coulomb binding of the hypothetical stable double-charged massive $O^{--}$ particles with nuclei of primordial helium. Such a dark matter can be captured by ordinary matter forming superheavy nuclei. We propose a possibility of self-bound by nuclear and electromagnetic interaction $O$-nuclearites as well as more massive gravitating ones and discuss effect of accumulation of $O$He atoms in stars and their effect in stellar evolution.

hep-ph↗

arXiv2019

Double charged heavy constituents of dark atoms and superheavy nuclear objects

We consider the model of composite dark matter assuming stable particles of charge $-2$ bound with primordial helium nuclei by Coulomb force in $O$He atoms. We study capture of such dark atoms in matter and propose a possibility of existence of stable $O$-enriched superheavy nuclei and $O$-nuclearites, in which heavy $O$-dark matter fermions are bound by electromagnetic forces with ordinary nuclear matter. $O$He atoms accumulation in stars and its possible effect in stellar evolution is also considered, extending the set of indirect probes for composite dark matter.

hep-ph↗

arXiv2018

Long-range interactions of kinks

We present a computational analysis of the long-range interactions of solitary waves in higher-order 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 (long-range 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 kink-antikink interactions in the example models via the method of collective coordinates.

hep-th↗

arXiv2018

A new look at the double sine-Gordon kink-antikink scattering

We study the kink-antikink scattering within the double sine-Gordon model. In the numerical simulations we found a critical value $v_{cr}$ of the initial velocity $v_{in}$, which separates two different scenarios: at $v_{in} v_{cr}$ the kinks pass through each other and escape to infinities. We obtain non-monotonous dependence of $v_{cr}$ on the model parameter $R$. Besides that, at some initial velocities below $v_{cr}$ we observe formation and interaction of the so-called oscillons (new phenomenon), as well as escape windows (well-known phenomenon).

hep-th↗

arXiv2018

Scattering of the $φ^8$ kinks with power-law asymptotics

We study the scattering of the $φ^8$ kinks off each other, namely, we consider those $φ^8$ kinks that have power-law asymptotics. The slow power-law fall-off leads to a long-range interaction between the kink and the antikink. We investigate how the scattering scenarios depend on the initial velocities of the colliding kinks. In particular, we observe the `escape windows' -- the escape of the kinks after two or more collisions, explained by the resonant energy exchange between the translational and vibrational modes. In order to elucidate this phenomenon, we also analyze the excitation spectra of a solitary kink and of a composite kink+antikink configuration.

hep-th↗

arXiv2018

Scattering of the double sine-Gordon kinks

We study the scattering of kink and antikink of the double sine-Gordon model. There is a critical value of the initial velocity $v_{cr}$ of the colliding kinks, which separates different regimes of the collision. At $v_{in}>v_{cr}$ we observe kinks reflection, while at $v_{in}<v_{cr}$ their interaction is complicated with capture and escape windows. We obtain the dependence of $v_{cr}$ on the parameter of the model. This dependence possesses a series of local maxima, which has not been reported by other authors. At some initial velocities below the critical value we observe a new phenomenon -- the escape of two oscillons in the final state. Besides that, at $v_{in}<v_{cr}$ we found the initial kinks' velocities at which the oscillons do not escape, and the final configuration looks like a bound state of two oscillons.

hep-th↗

arXiv2018

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

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 as their escape at some values of $v_{in}$.

hep-th↗

arXiv2018

Classical transitions with the topological number changing in the early Universe

We consider classical dynamics of two real scalar fields within a model with the potential having a saddle point. The solitons of such model are field configurations that have the form of closed loops in the field space. We study the formation and evolution of these solitons, in particular, the conditions at which they could be formed even when the model potential has only one minimum. These non-trivial field configurations represent domain walls in the three-dimensional physical space. The set of these configurations can be split into disjoint equivalence classes. We provide a simple expression for the winding number of an arbitrary closed loop in the field space and discuss the transitions that change the winding number. We also show that non-trivial field configurations could be responsible for the energy density excess that could evade the CMB constraints but could be important at scales which are responsible for the formation of galaxies and the massive primordial black holes.

hep-th↗

arXiv2017

Resonance phenomena in the $φ^8$ kinks scattering

We study the scattering of the $φ^8$ kinks with power-law asymptotics. We found two critical values of the initial velocity, $v_{cr}^{(1)}$ and $v_{cr}^{(2)}$, which separate different regimes of the kink-antikink collision. At the initial velocities $v_{in}< v_{cr}^{(1)}$ kinks can not collide due to repulsive force between them. At $v_{in}>v_{cr}^{(2)}$ the kinks escape to spatial infinities after one collision. In the range $v_{cr}^{(1)}\le v_{in}\le v_{cr}^{(2)}$ we observed kinks capture and formation of their bound state. Besides that, at these initial velocities we found resonance phenomena -- escape windows.

hep-th↗

arXiv2017

Transitions between topologically non-trivial configurations

We study formation and evolution of solitons within a model with two real scalar fields with the potential having a saddle point. The set of these configurations can be split into disjoint equivalence classes. We give a simple expression for the winding number of an arbitrary closed loop in the field space and discuss the evolution scenarios that change the winding number. These non-trivial field configurations lead to formation of the domain walls in the three-dimensional physical space.

hep-th↗

arXiv2017

Scattering of kinks in a non-polynomial model

We study a model described by a single real scalar field in the two-dimensional space-time. The model is specified by a potential which is non-polynomial and supports analytical kink-like solutions that are similar to the standard kink-like solutions that appear in the $φ^4$ model when it develops spontaneous symmetry breaking. We investigate the kink-antikink scattering problem in the non-polynomial model numerically and highlight some specific features, which are not present in the standard case.

hep-th↗

arXiv2017

Multi-kink collisions in the $ϕ^6$ model

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.

hep-th↗

arXiv2016

Three-body scattering problem in the fixed center approximation: the case of attraction

We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous -- they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, introducing a finite cut-off. We show that all three approaches are equivalent. We also discuss how our approach to the problem matches with the introduction of three-body contact interaction as done by other authors.

nucl-th↗

arXiv2016

Topological defects with power-law tails

We study interactions of kinks and antikinks of the $(1+1)$-dimensional $φ^8$ model. In this model, there are kinks with mixed tail asymptotics: power-law behavior at one infinity versus exponential decay towards the other. We show that if a kink and an antikink face each other in way such that their power-law tails determine the kink--antikink interaction, then the force of their interaction decays slowly, as some negative power of distance between them. We estimate the force numerically using the collective coordinate approximation, and analytically via Manton's method (making use of formulas derived for the kink and antikink tail asymptotics).

nlin.PS↗

arXiv2016

Scalar triplet on a domain wall: an exact solution

We study a model with a real scalar Higgs field and a scalar triplet field that allows existence of a topological defect -- a domain wall. The wall breaks the global $O(3)$ symmetry of the model, which gives rise to non-Abelian orientational degrees of freedom. We found an exact analytic solution that describes a domain wall with a localized configuration of the triplet field on it. This solution enables one to calculate contributions to the action from the orientational and translational degrees of freedom of the triplet field. We also study the linear stability of the domain wall with the triplet field switched off. We obtain that degrees of freedom localized on the wall can appear or do not appear depending on the parameters of the model.

hep-th↗