  Two deterministic models for Brownian motion are investigated by means of
numerical simulations and kinetic theory arguments. The first model consists of
a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks
acting as a thermal bath. The second is the same except for the shape of the
particles, which is now square. The basic difference of these two systems lies
in the interaction: hard core elastic collisions make the dynamics of the disks
chaotic whereas that of squares is not. Remarkably, this difference is not
reflected in the transport properties of the two systems: simulations show that
the diffusion coefficients, velocity correlations and response functions of the
heavy impurity are in agreement with kinetic theory for both the chaotic and
the non-chaotic model. The relaxation to equilibrium, however, is very
sensitive to the kind of interaction. These observations are used to reconsider
and discuss some issues connected to chaos, statistical mechanics and
diffusion.
