Nonlinear friction in a homogenous electron gas: Exact results

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Abstract
A model of an atom moving through a homogenous electron gas with a constant velocity is studied. The time-dependent Schrödinger equation is transformed into an equation with a time-independent Hamiltonian by means of a Galilei transformation. For the special case of noninteracting electrons the energy dissipation rate for arbitrary velocities is expressed in terms of the reflection coefficient in the one-dimensional case and in terms of the phase shifts in the three-dimensional case. The nonlinearity of the friction is discussed for special potentials.