Formation of a quasistationary state by scattering of wave packets on a finite lattice

Abstract

The formation and further evolution of the quasistationary state that accompanies the scattering of wave packets in one-dimensional finite periodic structures are studied. The contributions in the spectral integral from the saddle point and simultaneously from the poles of the stationary scattering amplitudes are estimated analytically. They can have the additive character and give different peaks in the secondary packets formed by the nonstationary wave function evolution. The lifetime of the quasistationary state is long and increases significantly with the lattice length especially near the thresholds of transmission bands.