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The ability for real-time control of topological defects can open upprospects for dynamical manipulation of macroscopic properties of solids. Asub-category of these defects, formed by particle dislocations, can beeffectively described using the Frenkel-Kontorova chain, which characterizesthe dynamics of these particles in a periodic lattice potential. This model isknown to host solitons, which are the topological defects of the system and arelinked to structural transitions in the chain. This work addresses three keyquestions: Firstly, we investigate how imperfections present in concreteimplementations of the model affect the properties of topological defects.Secondly, we explore how solitons can be injected after the rapid change inlattice potential or nucleated due to quantum fluctuations. Finally, we analyzethe propagation and scattering of solitons, examining the role of quantumfluctuations and imperfections in influencing these processes. Furthermore, weaddress the experimental implementation of the Frenkel-Kontorova model.Focusing on the trapped ion quantum simulator, we set the stage forcontrollable dynamics of topological excitations and their observation in thisplatform.

Dynamics of quantum discommensurations in the Frenkel-Kontorova chain