arXiv subjects
Publications and source records attributed to T. Romanczukiewicz.
We show that an oscillon can be understood as a localized discrete resonant (non-normalizable) mode. Specifically, oscillon in the vacuum arises from the threshold mode, which because of nonlinearity gets localized. Following this idea, we find {\it wobblerons} - nonlinear excitations of kinks, that is, oscillons-kink bound state. Now, the oscillon can also originate in an antibound mode, i.e., a discrete, positive energy but non-normalizable mode.
We consider a rational scalar field model in (1+1)-dimensions where the long-range character of the kinks is controllable. We show via numerical simulations that kinks with long-range tails on both sides can exhibit resonance windows. The resonant energy exchange mechanism occurs via the excitation of quasinormal modes, which we obtain via a spectral analysis. Additionally, we locate a resonance window in a family of $ϕ^{10}$ models with long-range tails on both sides. Moreover, we propose a new algorithm for initializing long-range kink collisions, based on convection-diffusion dynamics.
We show that in the complex $ϕ^6$ theory the oscillon, together with its spectral structure and the amplitude modulation, arises from the exited Q-ball carrying the bound and the quasi-normal modes.
In this paper, we explored a class of potentials with three minima that support kink solutions exhibiting one long-range tail. We analyzed antikink-kink interactions using an effective Lagrangian based on collective coordinates and compared the results to those obtained from full dynamical simulations. To this end, we constructed the collective coordinates with the antikink-kink configuration, and also a generalized Derrick mode, choosing the kink position and the Derrick mode amplitude as the moduli. For the antikink-kink configuration, we utilized the impurity ansatz proposed in \cite{campos2024collision}. We also studied the interaction of wobbling kinks where the lowest delocalized mode is excited.
We show that large scale oscillons, i.e., quasi-periodic, long living particle like solutions, may exist in massless theories, too. Their existence is explained using an effective (smeared) mass threshold which takes into account nonlinear (finite) perturbations.
We find that an oscillon can possess a characteristic double oscillation structure even though it results in a decay of a sphaleron which does not have any positive energy vibrational mode. We show that dynamics of such an oscillon can still be captured by collective coordinates provided by the sphaleron. Namely, its unstable mode and its scaling deformation i.e., Derrick mode.
We construct a simple field theory in which a sphaleron, i.e., a saddle-point particle-like solution, forms a semi-BPS state with a background defect that is an impurity. This means that there is no static force between the sphaleron and the impurity. Therefore such a sphaleron-impurity system is very much like usual BPS multi-solitons, however, still possessing an unstable direction allowing for its decay. We study dynamics of the sphaleron in such a system.
We analyze the perturbative Relativistic Moduli Space approach, where the amplitudes of the Derrick modes are promoted to collective coordinates. In particular, we analyse the possibility to calculate the critical velocity, i.e., the initial velocity of kinks at which single bounce scattering changes into a multi-bounce or annihilation collision, in the resulting Collective Coordinate Model (CCM). We find that for a growing number of modes the critical velocity of the CCM approaches the full field theory value. This is verified in the case of the $ϕ^4$ model, where we reach a $99\%$ accuracy. We also see such a convergence for a wide range of models belonging to the family of the double sine-Gordon and Christ-Lee theories, especially in those cases where the kinks do not reveal a too well pronounced half-kink inner structure.
We show that constrained $CP^1$ instantons, combined with the Relativistic Moduli Space approach, can accurately describe kink-antikink collisions in the $ϕ^4$ model.
We find that for various solitonic processes the corresponding canonical moduli space can have a boundary which is accessible in a finite time evolution. We show that such a boundary is not a failure of the moduli space approach but has a physical meaning. In our example, it corresponds to the complete annihilation of a colliding kink and antikink after a finite time. We further find that, close to the boundary, the solutions have an approximate self-similar form.
Antikink-kink ( $\bar{\rm K} $$ {\rm K}$) collisions in the $ϕ^6$ model exhibit resonant scattering although the $ϕ^6$ kinks do not support any bound states to which energy could be transferred. In Phys. Rev. Lett. 107 (2011) 091602 it was conjectured that, instead, energy is transferred to a collective bound mode of the full $\bar{\rm K} $$ {\rm K}$ configuration. Here we present further strong evidence for this conjecture. Further, we construct a collective coordinate model (CCM) for $\bar{\rm K} $$ {\rm K}$ scattering based on this collective bound mode trapped between the $\bar{\rm K} $$ {\rm K}$ pair which allows us to reproduce the full dynamics of $\bar{\rm K} $$ {\rm K}$ scattering with striking accuracy. We also study kink-antikink (${\rm K} $$ \bar{\rm K}$) scattering and its description by a CCM. In this case a significant role of radiation is discovered.
We show that thick spectral walls exist in antikink-kink collisions in the $ϕ^6$ model. In this model, they are triggered by the so-called $delocalized$ $modes$ which do not exist in the single-soliton sector but emerge in antikink-kink ($\bar{K}K$) collisions. Therefore, spectral walls are a rather common phenomenon that should occur in many solitonic collisions involving non-symmetric kinks as, e.g., in the $ϕ^8$ or higher power models.
The moduli space approximation to kink dynamics permits a relativistic generalization if the Derrick scaling parameter is used as a collective coordinate. We develop a perturbative approach to the resulting relativistic moduli space by expanding the Derrick scaling parameter about unity and treating the higher-order Derrick modes as new degrees of freedom. This approach allows us to resolve (coordinate) singularities order-by-order, and systematically incorporates relativistic corrections {\it perturbatively} in kink scattering. It gives an excellent description of kink-antikink collisions in $ϕ^4$ field theory already at first order, and at higher order, reproduces the fractal structure in the formation of the final state with an error of only $4\%$.
We show that in some kink-antikink (KAK) collisions sphalerons, i.e., unstable static solutions - rather than the asymptotic free soliton states - can be the source of the internal degrees of freedom (normal modes) which trigger the resonance phenomenon responsible for the fractal structure in the final state formation.
We show that spectral walls are common phenomena in the dynamics of kinks in (1+1) dimensions. They occur in models based on two or more scalar fields with a nonempty Bogomol'nyi-Prasam-Sommerfield (BPS) sector, hosting two zero modes, where they are one of the main factors governing the soliton dynamics. We also show that spectral walls appear as singularities of the dynamical vibrational moduli space.
The fractal velocity pattern in symmetric kink-antikink collisions in $ϕ^4$ theory is shown to emerge from a dynamical model with two effective moduli, the kink-antikink separation and the internal shape mode amplitude. The shape mode usefully approximates Lorentz contractions of the kink and antikink, and the previously problematic null-vector in the shape mode amplitude at zero separation is regularized.
We study kink-antikink scattering in a one-parameter variant of the $ϕ^4$ theory where the model parameter controls the static intersoliton force. We interpolate between the limit of no static force (BPS limit) and the regime where the static interaction is small (non-BPS). This allows us to study the impact of the strength of the intersoliton static force on the soliton dynamics. In particular, we analyze how the transition of a bound mode through the mass threshold affects the soliton dynamics in a generic process, i.e., when a static intersoliton force shows up. We show that the thin, precisely localized spectral wall which forms in the limit of no static force, broadens in a well-defined manner when a static force is included, giving rise to what we will call a thick spectral wall. This phenomenon just requires that a discrete mode crosses into the continuum at some intermediate stage of the dynamics and, therefore, should be observable in many soliton-antisoliton collisions.
We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy. These objects are, therefore, interpreted as totally incompressible solitons. As a first, particular example we consider (1+1) dimensional kinks in theories with a nonstandard kinetic term or, equivalently, in models with the so-called runaway (or vacummless) potentials. But incompressible solitons exist also in higher dimensions. As specific examples in (3+1) dimensions we study Skyrmions in the dielectric extensions both of the minimal and the BPS Skyrme models. In the the latter case, the skyrmionic matter describes a completely incompressible topological perfect fluid.