A localized perturbation moving through a homogeneous electron gas with a constant velocity is studied. The time-dependent Schr\"odinger equation is solved by means of a Galileo transformation. The energy dissipation rate is expressed in terms of the transport cross section for arbitrary velocities, temperatures, and strength of the perturbation. Expressions for the electron density and the backflow pattern around the moving perturbation are given. Quantitative results are presented for a hard-sphere potential.
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Bönig et al. (1989) studied this question.
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