The motion of a point charge near a two-dimensional periodic array of metallic islands has been studied. The appearance of 'image charges' in the neighborhood of the test charge not only affects its local electrostatic energy, but also its dynamical properties. We are interested in the effective dynamical behavior of the quasi-particle created this way, as it can dominate magneto-transport properties. The point charge is assumed to move on a plane parallel and very close to the two dimensional plane of the metallic islands. Through classical electromagnetic theory the response of the metallic islands due to the external charge is calculated for two different limits: First, square and spatially extended metallic islands with finite conductance are used. Second, and more appropriate to the 'far-field' description of the problem, islands are assumed to be well represented as classical dipoles which respond infinitely fast to the electrical field from the test point charge. We study the dynamically-averaged characteristics of the particle trajectories, such as energy and associated fields and potentials, in order to provide a classical evaluation of the effective mass of the test charge. [References: 4]
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