Autoresonant cooling of particles in spatially periodic potentials

The motion of an ensemble of noninteracting classical particles in a spatially periodic potential field has been considered, assuming that the ensemble initially undergoes ballistic motion. It is shown that an external perturbation in the form of a plane wave with adiabatically modulated frequency can lead to localization of a significant part of the ensemble with a decrease in the average energy of particles. The effect is related to the capture of particles in a chaotic layer in the phase space, which is induced by scattering on a resonance with the perturbation wave.