Non-Adiabatic Corrections to the Born-Oppenheimer Approximation in Classical Systems

We offer non-adiabatic corrections to the Born-Oppenheimer approximation when applied to classical systems of slow pistons coupled to fast gas particles. Using the recently developed Moving Born-Oppenheimer approximation, we see that the gas particles renormalize the effective mass of the pistons which leads to a modification of their frequency of oscillation about equilibrium. Moreover, in the case of multiple pistons, this mass renormalization is normal-mode dependent. We show agreement between our analytic results and simulations of exact dynamics.