We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear Schrodinger equation for the gauge field, and a linear equation for the scalar field containing the gauge field as a nonlinear source. This equation is used to predict the existence of oscillons and oscillating kinks for certain regimes of the ratio of the Higgs to the gauge field masses. Results of direct numerical simulations are found to be in very good agreement with the analytical findings, and show that the oscillons are robust, while kinks are unstable. It is also demonstrated that oscillons emerge spontaneously as a result of the onset of the modulational instability of plane wave solutions of the model. Connections of the results with the phenomenology of superconductors is discussed.
We study compact kinks and its interaction with compact oscillons in models with non-analytic potentials. Oscillon-like excitations are the main ingredients of the radiation field. We look at the problem of scattering which involves topological compact kinks and non-topological oscillons. We also look at the problem of propagation of small perturbation at the kink bulk.
Scattering of kinks in Frankensteinian potentials: Kinks as bubbles of exotic mass and phase transitions in oscillon production
Institute of Physics, Silesian University in Opava（奥帕瓦西里西亚大学物理研究所）；Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava（奥帕瓦西里西亚大学物理研究所理论物理与天体物理研究中心）
Oscillons are time-dependent, localized in space, extremely long-lived states in nonlinear scalar-field models, while kinks are topological solitons in one spatial dimension. In the present work, we show new classes of oscillons and oscillating kinks in a system of two nonlinearly coupled scalar fields in $1 + 1$ spatiotemporal dimensions. The solutions contain a control parameter, the variation of which produces oscillons and kinks with a flat-top shape. The model finds applications to condensed matter, cosmology, and high-energy physics.
We study final states in the scattering of kinks and antikinks of the $φ^8$ field-theoretic model. We use the initial conditions in the form of two, three or four static or moving kinks. In the numerical experiments we observe a number of different processes such as emergence of static and moving oscillons, change of the kink's topological sector, scattering of an oscillon by a kink, production of kink-antikink pairs in oscillon-oscillon collisions. In antikink-kink collisions for asymmetric kinks, we found resonance phenomena -- escape windows.
We present a numerical study of the process of production of kink-antikink pairs in the collision of particle-like states in the one-dimensional $ϕ^4$ model. It is shown that there are 3 steps in the process, the first step is to excite the oscillon intermediate state in the particle collision, the second step is a resonance excitation of the oscillon by the incoming perturbations, and finally, the soliton-antisoliton pair can be created from the resonantly excited oscillon. It is shown that the process depends fractally on the amplitude of the perturbations and the wave number of the perturba…
Recent studies have emphasized the important role that a shape deformability of scalar-field models pertaining to the same class with the standard $ϕ^4$ field, can play in controlling the production of a specific type of breathing bound states so-called oscillons. In the context of cosmology, the built-in mechanism of oscillons suggests that they can affect the standard picture of scalar ultra-light dark matter. In the present work kink scatterings are investigated in a parametrized model of bistable system admitting the classical $ϕ^4$ field as an asymptotic limit, with focus on the formation…
We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear Schrödinger equation for the gauge field, and a linear equation for the scalar field containing the gauge field as a nonlinear source. This equation is used to predict the existence of oscillons and oscillating kinks for certain regimes of the ratio of the Higgs to the gauge field masses. Results of numerical simulations are found to be in very good agreement with th…
In this work we examine kink-antikink collisions in two distinct hyperbolic models. The models depend on a deformation parameter, which controls two main characteristics of the potential with two degenerate minima: the height of the barrier and the values of the minima. In particular, the rest mass of the kinks decreases monotonically as the deformation parameter increases, and we identify the appearance of a gradual suppression of two bounce windows in the kink scattering and the production of long lived oscillons. The two effects are reported in connection to the presence of more than one vi…
Research Center for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava（奥帕瓦西莱西亚大学物理学院理论物理与天体物理学研究中心）；Institute of Experimental and Applied Physics, Czech Technical University in Prague（布拉格捷克理工大学实验与应用物理研究所）；Institute of Theoretical Physics, Jagiellonian University（雅盖隆大学理论物理研究所）；International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM 2 ), Hiroshima University（广岛大学缠结手性超物质可持续发展国际研究所）
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 --…
We study the classical dynamics of the Abelian-Higgs model in (1+1) space-time dimensions bf for the case of strongly broken gauge symmetry. In this limit the wells of the potential are almost harmonic and sufficiently deep, presenting a scenario far from the associated critical point. Using a multiscale perturbation expansion, the equations of motion for the fields are reduced to a system of coupled nonlinear Schrodinger equations (CNLS). Exact solutions of the latter are used to obtain approximate analytical solutions for the full dynamics of both the gauge and Higgs field in the form of osc…
We have investigated the head-on collision of a two-kink and a two-antikink pair that arises as a generalization of the $ϕ^4$ model. We have evolved numerically the Klein-Gordon equation with a new spectral algorithm whose accuracy and convergence were attested by the numerical tests. As a general result, the two-kink pair is annihilated radiating away most of the scalar field. It is possible the production of oscillons-like configurations after the collision that bounce and coalesce to form a small amplitude oscillon at the origin. The new feature is the formation of a sequence of quasi-stati…
This paper investigates a model containing $ϕ^4$ kinks interacting with fermions. The fermion back-reaction is included in the equations of motion, which affects the kink-antikink collisions. We show that the fermion field generates a force that can be either attractive or repulsive. Moreover, we investigate three different scenarios, which exhibit a wide variety of behaviors including the usual scenarios observed in the $ϕ^4$ model as well as the formation of two oscillons, reflection without contact, one-bounce resonance windows, and the creation of kink-antikink pairs. We also find evidence…
We present a comprehensive, nonperturbative analytical method to investigate the dynamics of time-dependent oscillating scalar field configurations. The method is applied to oscillons in a double well Klein-Gordon model in two and three spatial dimensions, yielding high accuracy results in the characterization of all aspects of the complex oscillon dynamics. In particular, we show how oscillons can be interpreted as long-lived perturbations about an attractor in field configuration space. By investigating their radiation rate as they approach the attractor, we obtain an accurate estimate of th…
In this work we consider model of asymmetric kinks, where the behavior of the solution in one side is different from the other side. Also, the models depend of an integer $n$ and, with the increase of $n$, the constructed kink assumes a hybrid character: a compactlike profile on one side and a kinklike profile on the other side. We investigate numerically the kink-antikink and antikink-kink dynamics, with the aim to understand the effect of the transition of the usual kink to the semi-compacton structure. The kink-antikink process shows the formation of one-bounce windows for small values of $…
The `mechanization' is a procedure of replacing a scalar field in 1+1 dimensions with a piece-wise linear function, i.e. a finite graph consisting of $N$ joints (vertices) and straight segments (edges). As a result, the field theory is approximated by a sequence of algebraically tractable, general-purpose collective coordinate mechanical models. We observe the step-by-step emergence of dynamical objects and associated phenomena as the $N$ increases. Mech-kinks and mech-oscillons -- mechanical analogs of kinks and oscillons (bions) -- appear in the simplest models, while more intricate dynamica…
I-ball/oscillon is a soliton-like oscillating configuration of a real scalar field which lasts for a long time. I-ball/oscillon is a minimum energy state for a given adiabatic invariant, and its approximate conservation guarantees the longevity. In this paper, we examine the stability of a special type of I-ball/oscillon, the "exact" I-ball/oscillon, whose adiabatic invariant is exactly conserved. We show that the exact I-ball/oscillon is stable in classical field theory, but not stable against small perturbations depending on the value of its adiabatic invariant. Accordingly, the exact I-ball…
Numerical simulations show that a massive real scalar field in a nonlinear theory can form long-lived oscillating localized states. For a self-interacting scalar on a fixed background these objects are named oscillons, while for the self-gravitating case they are called oscillatons. This extensive review is about the history and various general properties of these solutions, though mainly focusing on the small but nonzero classical scalar field radiation emitted by them. The radiation for higher amplitude states can be calculated by a spectral numerical method. For small and moderately large a…
Many classical scalar field theories possess remarkable solutions: coherently oscillating, localized clumps, known as oscillons. In many cases, the decay rate of classical small amplitude oscillons is known to be exponentially suppressed and so they are extremely long lived. In this work we compute the decay rate of quantized oscillons. We find it to be a power law in the amplitude and couplings of the theory. Therefore, the quantum decay rate is very different to the classical decay rate and is often dominant. We show that essentially all oscillons eventually decay by producing outgoing radia…
A generic feature of string compactifications is the presence of many scalar fields, called moduli. Moduli are usually displaced from their post-inflationary minimum during inflation. Their relaxation to the minimum could lead to the production of oscillons: localised, long-lived, non-linear excitations of the scalar fields. Here we discuss under which conditions oscillons can be produced in string cosmology and illustrate their production and potential phenomenology with two explicit examples: the case of an initially displaced volume modulus in the KKLT scenario and the case of a displaced b…
In this work we investigate the consequences of the Lorentz symmetry violation on extremely long-living, time-dependent, and spatially localized field configurations, named oscillons. This is accomplished in ($D+1$) dimensions for two interacting scalar field theories in the so-called Standard Model-Extension context. We show that $D$-dimensional scalar field lumps can present a typical size $R_{\min }\ll R_{KK}$, where $R_{KK}$ is the associated length scale of extra dimensions in Kaluza-Klein theories. Here, the size $R_{\min }$ is shown to strongly depend on the terms that control the Loren…
The radiation from oscillating kink in (1+1) dimensional relativistic $ϕ^4$ model is considered. Both analytical and numerical approaches are presented and the comparison between these methods is discussed. Acceleration of the kink in external radiation is calculated and numerical results are also presented.
The charged, spinning and gravitating soliton is realized as a regular solution of the Kerr-Newman field coupled with a chiral Higgs model. A regular core of the solution is formed by a domain wall bubble interpolating between the external Kerr-Newman solution and a flat superconducting interior. An internal electromagnetic (em) field is expelled to the boundary of the bubble by the Higgs field. The solution reveals two new peculiarities: (i) the Higgs field is oscillating, similar to the known oscillon models, (ii) the em field forms on the edge of the bubble a Wilson loop, resulting in quant…
