Relativistic moduli space and critical velocity in kink collisions.

One important tool in the analysis of the collision of kinks and other topological solitons is the reduction of the original field theory to a finite-dimensional system of so-called collective coordinates. Here we study one recent proposal of a collective coordinate model (CCM), the perturbative relativistic moduli space (pRMS), where the amplitudes of the Derrick modes are promoted to collective coordinates. In particular, we analyze the possibility to calculate within the pRMS the critical velocity, i.e., the initial velocity of kinks at which single bounce scattering changes into a multibounce or annihilation collision. We find that for a growing number of Derrick modes the critical velocity of the CCM approaches the full field theory value. In particular, in the case of the ϕ^{4} model we reach a 99% accuracy. We also see this 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.

Semi-Bogomol'nyi-Prasad-Sommerfield sphaleron and its dynamics.

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 multisolitons, however, still possessing an unstable direction allowing for its decay. We study dynamics of the sphaleron in such a system.

Collective Coordinate Model of Kink-Antikink Collisions in ϕ

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.

Kink-antikink collisions in a weakly interacting ϕ

Kink-antikink scattering in nonintegrable field theories like ϕ^{4} theory is still rather poorly understood beyond brute-force numerical calculations, even after several decades of investigation. Recently, however, some progress has been made based on the introduction of certain self-dual background fields in these field theories which imply both the existence of static kink-antikink solutions of the Bogomol'nyi type and the possibility of an adiabatic scattering (moduli space approximation). Here we continue and generalize these investigations by introducing a one-parameter family of models interpolating between the Bogomol'nyi-Prasad-Sommerfield (BPS) model with the self-dual background field and the original ϕ^{4} theory. More concretely, we study kink-antikink scattering in a parameter range between the limit of no static force (BPS limit) and the regime where the static interaction between kink and antikink is small (non-BPS regime). 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 call a thick spectral wall. This phenomenon results from the appearance of a stationary saddle point solution where the acceleration of the solitons owing to the attractive force is compensated by the dynamics of the sufficiently excited mode. Thus, this barrier shows up before the mode crosses the mass threshold.

Spectral Walls in Soliton Collisions.

During defect-antidefect scattering, bound modes frequently disappear into the continuous spectrum before the defects themselves collide. This leads to a structural, nonperturbative change in the spectrum of small excitations. Sometimes the effect can be seen as a hard wall from which the defect can bounce off. We show the existence of these spectral walls and study their properties in the ϕ^{4} model with Bogomol'nyi-Prasad-Sommerfield preserving impurity, where the spectral wall phenomenon can be isolated because the static force between the antikink and the impurity vanishes. We conclude that such spectral walls should surround all solitons possessing internal modes.

Bogomol'nyi-Prasad-Sommerfield Skyrme model and nuclear binding energies.

We use the classical Bogomol'nyi-Prasad-Sommerfield (BPS) soliton solutions of the BPS Skyrme model together with corrections from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies, and a small explicit breaking of the isospin symmetry-accounting for the proton-neutron mass difference-to calculate nuclear binding energies. We find that the resulting binding energies are already in excellent agreement with their physical values for heavier nuclei, demonstrating thereby that the BPS Skyrme model is a distinguished starting point for a detailed quantitative investigation of nuclear and low-energy strong interaction physics.