  Like ants, some microorganisms are known to leave trails on surfaces to
communicate. We explore how trail-mediated self-interaction could affect the
behavior of individual microorganisms when diffusive spreading of the trail is
negligible on the timescale of the microorganism using a simple
phenomenological model for an actively moving particle and a finite-width
trail. The effective dynamics of each microorganism takes on the form of a
stochastic integral equation with the trail interaction appearing in the form
of short-term memory. For moderate coupling strength below an emergent critical
value, the dynamics exhibits effective diffusion in both orientation and
position after a phase of superdiffusive reorientation. We report experimental
verification of a seemingly counterintuitive perpendicular alignment mechanism
that emerges from the model.
