Dynamics of quasiparticles in a nonstationary random field

The problem of nonlinear absorption of a stochastic acoustic signal in superconductors is reduced to an investigation of the states of the one-dimensional Dirac equation in a coordinate system moving with constant velocity and with a random potential [1,2]. In the present paper a study is made of the properties of the problem of scattering by a random potential that determine the rate of dissipation of the acoustic energy and also of the localized properties of solutions in the case of an infinitely extended signal. If the projection of the Fermi velocity of an electron onto the direction of propagation of the signal is less than the velocity of sound, then all states in the field of an infinitely extended signal are localized (there is a purely point spectrum), and the mean coefficient of transmission of an electron through the region occupied by the sound is exponentially small for a sufficiently long signal. In the opposite case all states are delocalized (the spectrum is absolutely continuous), and on scattering reflection is replaced by partial transformation, for which the mean coefficient of disbalance is exponentially small for a sufficiently long signal.