  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.
