Kinetic Equation for the Electron-Phonon Gas

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Abstract
The random phase approximation equations of motion for the electron-phonon system are solved to obtain long-time expressions for the basic operators that appear in the calculation of correlation functions. These operator expressions are used to obtain a kinetic equation for the electrons and an expression for the phonon spectral function. The kinetic equation has the same form as the Balescu-Lenard equation. Expressions for the density autocorrelation function and the two-particle correlation function are also obtained. The latter is shown to have the same form as the test-particle result for a classical plasma.