We present a model for the scaling laws of the electric field noise spectral density as a function of the distance d above a conducting surface. Our analytical approach models the patch potentials by introducing a correlation length ζ of the electric potential on the surface. The predicted scaling laws are in excellent agreement with two different classes of experiments (cold trapped ions and cantilevers), for which the d parameter differs by four orders of magnitude. According to this model, heating rate in miniature ion traps could be greatly reduced by proper material engineering.
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Dubessy et al. (2009) studied this question.
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