Spatially Inhomogeneous Phonon Amplification in Solids

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Abstract
A theory is presented for acoustic domains of both the stationary and propagating kinds. In the latter case, a mechanism of domain generation is also given. The basic assumption of the theory is that the spatially inhomogeneous amplification can be described by the stimulated emission of incoherent phonons within individual, macroscopic volume elements. By taking appropriate moments of the Boltzmann equations of the electron-phonon system, generalized to include drift terms, a set of three coupled integrodifferential equations is obtained. With suitable boundary conditions, these equations determine the three unknowns—drift velocity, phonon number, and macroscopic electric field—as a function of position and time. Some applications of the equations are given, and possible future applications are outlined.