  We consider the dynamics of Dirac particles moving in the curved spaces with
one coordinate subjected to compactification and thus interpolating smoothly
between three- and two-dimensional spaces. We use the model of
compactification, which allows us to perform the exact Foldy-Wouthuysen
transformation of the Dirac equation and then to obtain the exact solutions of
the equations of motion for momentum and spin in the classical limit. The spin
precesses with the variable angular velocity, and a "flick" may appear in the
remnant two-dimensional space once or twice during the period. We note an
irreversibility in the particle dynamics because the particle can always
penetrate from the lower-dimensional region to the higher-dimensional region,
but not inversely.
