Classical freezing of plane rotations : a proof of the Boltzmann-jeans conjecture

摘要: Using simple known methods and results of classical perturbation theory, especially those due to Nekhoroshev Neishtadt, we study the energy exchanges between rotational translational degrees freedom in a particular model representing planar motion rigid body bounded analytic potential. We prove that, if angular velocity co is initially large, then are small, O(co 1), for times growing exponentially with co, Ill ~ exp co. also deduce that scattering process from (smooth) potential barrier, overall change incoming small g exp(-co). The interpreted light an old conjecture by Boltzmann Jeans on existence very large time scales equilibrium statistical systems containing high-frequency (purely "freezing" freedom); rotating object is, this interpretation, (classical) molecule, which moves external field, or collides wall container. Two different limits considered, namely limit energy, (as interesting molecular interpretation) point mass, at finite energy.