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We present and study new mechanism of interaction between the solitons based on the exchange interaction mediated by the localized fermion states. As particular examples, we consider solutions of simple 1+1 dimensional scalar field theories with self-interaction potentials, including sine-Gordon model and the polynomial $phi^4$, $phi^6$ models, coupled to the Dirac fermions with back-reaction. We discover that there is an additional fermion exchange interaction between the solitons, it leads to the formation of static multi-soliton bound states. Further, we argue that similar mechanisms of formation of stable coupled multi-soliton configurations can be observed for a wide class of physical systems.
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The system consisting of a fermion in the background of a wobbling kink is studied in this paper. To investigate the impact of the wobbling on the fermion-kink interaction, we employ the time-dependent perturbation theory formalism in quantum mechanics. To do so, we compute the transition probabilities between states given in terms of the Bogoliubov coefficients. We derive Fermis golden rule for the model, which allows the transition to the continuum at a constant rate if the fermion-kink coupling constant is smaller than the wobbling frequency. Moreover, we study the system replacing the shape mode with a quasinormal mode. In this case, the transition rate to continuum decays in time due to the leakage of the mode, and the final transition probability decreases sharply for large coupling constants in a way that is analogous to Fermis golden rule. Throughout the paper, we compare the perturbative results with numerical simulations and show that they are in good agreement.
In this paper the scattering between a wobbling kink and a wobbling antikink in the standard $phi^4$ model is numerically investigated. The dependence of the final velocities, wobbling amplitudes and frequencies of the scattered kinks on the collision velocity and on the initial wobbling amplitude is discussed. The fractal structure becomes more intricate due to the emergence of new resonance windows and the splitting of those arising in the non-excited kink scattering. Outside this phase the final wobbling amplitude exhibits a linear dependence of the collision velocity whereas the final frequency is a decreasing function. By contrast these magnitudes are almost independent of the initial wobbling amplitude.
Sine-Gordon kinks are a much studied integrable system that possesses multi-soliton solutions. Recent studies on sine-Gordon kinks with space-dependent square-well-type potentials have revealed interesting dynamics of a single kink interacting with wells and barriers. In this paper, we study a class of smooth space-dependent potentials and discuss the dynamics of one kink in the presence of different wells. We also present values for the critical velocity for different types of barriers. Furthermore, we study two kinks interacting with various wells and describe interesting trajectories such as double-trapping, kink knock-out and double-escape.
We study the creation of solitons from particles, using the $lambda phi^4$ model as a prototype. We consider the scattering of small, identical, wave pulses, that are equivalent to a sequence of particles, and find that kink-antikink pairs are created for a large region in parameter space. We also find that scattering at {it low} velocities is favorable for creating solitons that have large energy compared to the mass of a particle.
A first order equation for a static ${phi}^4$ kink in the presence of an impurity is extended into an iterative scheme. At the first iteration, the solution is the standard kink, but at the second iteration the kink impurity generates a kink-antikink solution or a bump solution, depending on a constant of integration. The third iterate can be a kink-antikink-kink solution or a single kink modified by a variant of the kinks shape mode. All equations are first order ODEs, so the nth iterate has n moduli, and it is proposed that the moduli space could be used to model the dynamics of n kinks and antikinks. Curiously, fixed points of the iteration are ${phi}^6$ kinks.
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