Interaction between charged particle and strained superlattice and chaotic behaviours of the system

The effect on a particle motion of a deflecting channel is equated to modulation by a weak-periodic potential of similar shape as the channel. The motion equation of a particle is reduced to the nonlinear differential equation with a weak-periodic modulation by sine-squared potential. The critical conditions for the revelation of Smale horseshoe are analyzed using the Melnikov method. It is predicted that the chaotic behaviours may exit in the interaction of a particles between a crystal. Theory is provided to describe PME effects for the semicoductor superlattice.