Classical Freezing of Fast Rotations - A Numerical Test of the Boltzmann-jeans Conjecture

We study numerically a very simple model representing a classical planar molecule, with only translational and rotational degrees of freedom, which collides with a fixed wall. On this model we test numerically an old conjecture by Boltzmann and Jeans, according to which the rate of the energy exchanges between the translational and the rotational degrees of freedom, due to collisions, decreases exponentially with the angular velocity of the molecule, giving rise to a purely classical phenomenon of "freezing" of fast rotations. Our results are in full agreement with the Boltzmann-Jeans conjecture. More precisely, we find that for each collision the average on the initial phase of the energy exchange, and the fluctuation, follow two different exponential laws; this fact turns out to have a rather delicate role in the approach of statistical equilibrium. A discussion of the numerical accuracy-which is rather high, since we are able to measure energy exchanges of one part over 10(16)-is also reported.