Dressed-particle approach in the nonrelativistic classical limit

For a nonrelativistic classical particle undergoing arbitrary oscillations, the generalized effective potential Y is derived from nonlinear eigenfrequencies of the particle-field system. Specifically, the ponderomotive potential is extended to a nonlinear oscillator, resulting in multiple branches near the primary resonance. For a pair of natural frequencies in a beat resonance, Y scales linearly with the internal actions and is analogous to the dipole potential for a two-level quantum system. Thus cold quantum particles and highly-excited quasiclassical objects permit uniform manipulation tools, particularly, one-way walls.