  A self-propelled artificial microswimmer is often modeled as a ballistic
Brownian particle moving with constant speed aligned along one of its axis, but
changing direction due to random collisions with the environment. Similarly to
thermal noise, its angular randomization is described as a memoryless
stochastic process. Here, we speculate that finite-time correlations in the
orientational dynamics can affect the swimmer's diffusivity. To this purpose we
propose and solve two alternative models. In the first one we simply assume
that the environmental fluctuations governing the swimmer's propulsion are
exponentially correlated in time, whereas in the second one we account for
possible damped fluctuations of the propulsion velocity around the swimmer's
axis. The corresponding swimmer's diffusion constants are predicted to get,
respectively, enhanced or suppressed upon increasing the model memory time.
Possible consequences of this effect on the interpretation of the experimental
data are discussed.
