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Register a new userDynamics of multi-kinks in the presence of wells and barriers
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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.
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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.
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.
We consider the existence and spectral stability of static multi-kink structures in the discrete sine-Gordon equation, as a representative example of the family of discrete Klein-Gordon models. The multi-kinks are constructed using Lins method from an alternating sequence of well-separated kink and antikink solutions. We then locate the point spectrum associated with these multi-kink solutions by reducing the spectral problem to a matrix equation. For an $m$-structure multi-kink, there will be $m$ eigenvalues in the point spectrum near each eigenvalue of the primary kink, and, as long as the spectrum of the primary kink is imaginary, the spectrum of the multi-kink will be as well. We obtain analytic expressions for the eigenvalues of a multi-kink in terms of the eigenvalues and corresponding eigenfunctions of the primary kink, and these are in very good agreement with numerical results. We also perform numerical time-stepping experiments on perturbations of multi-kinks, and the outcomes of these simulations are interpreted using the spectral results.
We investigate numerically kink collisions in a $1+1$ dimensional scalar field theory with multiple vacua. The domain wall model we are interested in involves two scalar fields and a potential term built from an asymmetric double well and (double) sine-Gordon potential together with an interaction term. Depending on the initial kink setup and impact velocities, the model allows for a wide range of scattering behaviours. Kinks can repel each other, annihilate, form true or false domain walls and reflect off each other.
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.
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