Dressed-particle approach in the nonrelativistic classical limit

TL;DR

This paper derives a generalized effective potential for nonrelativistic classical particles with oscillations, extending ponderomotive potential concepts to nonlinear systems and linking classical and quantum manipulation techniques.

Contribution

It introduces a nonlinear eigenfrequency-based effective potential applicable to arbitrary oscillating particles, bridging classical and quantum manipulation methods.

Findings

Derived the generalized effective potential Y from nonlinear eigenfrequencies.

Extended the ponderomotive potential to nonlinear oscillators with multiple branches.

Showed Y scales linearly with internal actions near beat resonance, analogous to quantum dipole potential.

Abstract

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.