Injection and nucleation of topological defects in the quench dynamics of the Frenkel-Kontorova model

We explore the dynamics of a commensurate-incommensurate (C-IC) transition in a one-dimensional Frenkel-Kontorova chain. An incommensurate ratio between the period of the trapping potential and the average inter-particle distance, triggers a rearrangement of the atoms in a configuration where they occupy positions dislocated from the potential minima. We show that the transition mirrors in non-equilibrium dynamics with a mechanism of discrete injection of atomic discommensurations, which enter from the edges of the chain in a stepwise fashion. Furthermore, when the system is quenched close to the boundary of the C-IC transition, quantum fluctuations can have deep impact on dynamics resulting in a response characterized by the superposition of commensurate and incommensurate configurations of the chain. The motion of discommensurations can be exactly mapped to the dynamics of solitons travelling along the chain, allowing us to explore mechanisms for discrete injection and nucleation of topological structures in our model. We also offer concrete perspectives for implementing the dynamics of these topological defects in trapped ions experiments.