Exponential growth and possible condensation of the particle-hole excitations in moving hot Fermi liquids

The production rate of particle-antiparticle and particle-hole excitations in relativistically moving hot Fermi liquids is calculated. The kinetics of the damping of the excitations as well as of the exponential growth of the particle-hole excitations for some regions of space-like momenta is considered, in the center of mass coordinate projected along the quasi-particle current direction. It is shown that Cherenkov-like radiation of the excitations may form a Bose condensate with a non-zero wave vector. Explicit results are presented for pions and for various types of zero sounds in moving hot nuclear matter.