Non-equilibrium phonon distribution caused by an electrical current

Abstract In an attempt to explain flash sintering experiments, it had been proposed that the electron–phonon coupling leads a proliferation of short wave-length lattice vibrations in electric field. this paper we investigate by solving two coupled Boltzmann equations, describing free electron gas field scattering from crystal heat bath. The imposes cylindrical symmetry and drives electrons phonons into non-equilibrium steady state. We find phonon distribution shows strong excess population at Brillouin zone edge direction argue analytically, can be traced back shifted Fermi sphere for electrons. Furthermore, not only energy but also momentum is exchanged system, which defies any system two-temperature model.