Abstract
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.
Highlights
We show the existence of these spectral walls and study their properties in the φ4 model with Bogomol’nyiPrasad-Sommerfield preserving impurity, where the spectral wall phenomenon can be isolated because the static force between the antikink and the impurity vanishes
Spectral wall.—We have collided the BPS antikink initially separated by að0Þ 1⁄4 −10 with the impurity for α 1⁄4 0.3 and α 1⁄4 3.0 (Fig. 3)
Summary.—In this Letter, we investigated in detail how soliton scattering is affected by the interaction of the colliding solitons with an internal, vibrational mode, in particular, when this mode disappears into the continuum
Summary
Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782 Santiago de Compostela, Spain. The prototypical φ4 model in 1 þ 1 dimensions, e.g., reveals kink-antikink collisions with a chaotic structure, typically associated with the existence of one or several internal modes which may be excited during the scattering process [1,2,3,4,5] These modes can store energy, binding the solitons for a while, and may eventually transfer their energy back to the translational degrees of freedom. Even beyond the effective model, the mixing of the kink-mode interaction with the (static) forces between solitons, which change the soliton profiles and their spectral properties, renders any analytical treatment very difficult. This mixing problem could be avoided for a theory with static multisoliton solutions of the Bogomol’nyi-PrasadSommerfield (BPS) type. Individual solitons of a static multisoliton configuration do not interact, like, e.g., 0031-9007=19=122(24)=241601(5)
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