  In this paper we investigate the Quantum Brownian motion of a point particle
induced by quantum vacuum fluctuations of a massless scalar field in (3 +
1)-dimensional Minkowski spacetime with distinct conditions (Dirichlet,
Neumann, mixed and quasiperiodic). The modes of the field are confined and
compactified to a finite length region, which consequently provides a natural
measure scale for the system. Useful expressions for the Wightman function have
been obtained, which allow us to calculate analytical expressions for the
velocity dispersion in all condition cases considered. We also obtain
expressions for the velocity dispersion in the short and late time regimes.
Finally, we exhibit some graphs in order to show the behavior of the velocity
dispersions, discussing important divergencies that are present in our results.
