| Abstract: | Consider a classical particle and a generic quantum system that are mutually coupled. A common scenario is that the Hamiltonian operator depends parametrically on the particle coordinate and at the same time the particle experiences an Ehrenfest-type force. If the classical particle moves slowly, it drives the quantum system adiabatically. I derive an effective equation of motion for the classical particle to third order in its velocity. This is achieved through a formulation of adiabatic perturbation theory that makes essential use of the quantum covariant derivative - a geometric structure induced by the position-dependence of the adiabatic eigenstate. The third-order equation contains corrections to the effective mass tensor and the curvature of the gauge field, as well as additional terms not seen before. I will report numerical simulations exploring the qualitative effect of the third-order terms. |