Theory of fluctuations in non-equilibrium electron—hot-phonon system

A new type of correlation caused by fluctuations is resolved in coupled nonequilibrium (hot) electron-phonon system described by Boltzmann and Planck statistics. The kinetic equation for equal-time electron-phonon correlation function is obtained from the first principles by diagram technique. The correlation is demonstrated through Monte Carlo simulation of hot-electron-hot-phonon interaction in GaN subjected to a strong electric field. Hot-phonon lifetime can be obtained from hot-electron fluctuations.