The effect of double frequency oftrap field φ = U - V1 cos Ωt - V2 cos 2Ωt in a Paul trap can be described exactly by using a function series expansion to so
A method of solving an ultracold trapped ion at the node of the standing wave laser without rotating wave approximation is proposed and the analytical forms of
Theoretical analysis of the DNA dynamics reveals that interaction between the single solitons and plane wave implies Smale-horseshoe chaos in the double helices