Momentum of a fast particle in a dissipative medium with an excitation threshold

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Abstract
Using a quantum mechanical non-equilibrium formalism, the momentum distribution of an electron is evaluated for various times after it has been inserted with a given momentum into a dissipative medium. The medium is assumed to have an excitation threshold, and so might represent plasmons or optical phonons. The initial momentum of the electron is taken to be large, allowing an approximation based on the neglect of recoil correlations to be used. The distributions obtained are compared with those resulting from the Boltzmann equation, and the effects of virtual processes and of recoil correlations illustrated. At short times, considerable differences from the Boltzmann predictions are seen. At longer times, the distributions approach the Boltzmann predictions if the coupling of the electron to the medium is weak.