Abstract
We numerically study the structure and the normal-mode spectrum of two vertically coupled finite-size two-dimensional systems of interacting classical charged particles that are confined by a nonuniform distribution of background charge. The structural and dynamical properties of the system are analyzed as a function of the separation between the planes of charges $(d)$, as well as a function of the strength of the confinement potential $(Z)$. We find different asymmetrical ground-state configurations, as well as structural phase transitions induced by the unbinding of particles, which were not present in previous models with a parabolic confinement potential. Depending on the order of the structural transition the normal-mode frequencies exhibit a discontinuity or a softening.
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