| Summary: | Non-adiabatic crossing of symmetry breaking phase transitions results in formation of a domain structure and topological defects. The average density of domains depends on the quench rate of the phase transition. Kibble-Zurek mechanism predicts the scaling of the number of domains with quench rate. Phase transitions are ubiquitous in Nature and formation of domains and defects occurs in many different systems. One example of such system is Coulomb crystals of trapped ions, where structural defects can form as a result of symmetry breaking structural transitions between different crystal configurations. In the thesis, we investigate the Kibble-Zurek mechanism using the linear to zigzag structural phase transition in trapped ion Coulomb crystals. First, we analyse the equilibrium properties of crystals in the vicinity of the critical point of the linear to zigzag transition. Next, we show how to derive Kibble-Zurek scaling laws by transforming the equations of motion into a universal form. This mathematical derivation of the scaling laws is generalized for finite and inhomogeneous systems. Two experiments measuring the defect scaling in small trapped ion crystals are described, whose results agree with molecular dynamics simulations. In order to understand and predict defect dynamics we develop the technique for calculating the effective potential in which the defects move. Using this technique we show that heavy molecular ions stabilize the structural defects in zigzag chains and suggest a way of controlling kink motion using the application of electric fields. Finally, conclusions are drawn and possibilities for future work are suggested.
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