Relaxation properties in classical diamagnetism

In the present paper the problem of the relaxation of magnetization to equilibrium (i.e., with no magnetization) is investigated numerically for a variant of the well-known model introduced by Bohr to study the diamagnetism of electrons in metals. Such a model is mathematically equivalent to a billiard with obstacles in a magnetic field. We show that it is not guaranteed that equilibrium is attained within the typical time scales of microscopic dynamics. Indeed, considering an out of equilibrium state produced by an adiabatic switching on of a magnetic field, we show that, depending on the values of the parameters, one has a relaxation either to equilibrium or to a diamagnetic (presumably metastable) state. The analogy with the relaxation properties in the FPU problem is also pointed out.