Title: Delay sober up drunkers: Control of diffusion in random walkers,
Abstract: Time delay in general leads to instability in some systems, while a specific
feedback with delay can control fluctuated motion in nonlinear deterministic
systems to a stable state. In this paper, we consider a non-stationary
stochastic process, i.e., a random walk and observe its diffusion phenomenon
with time delayed feedback. Surprisingly, the diffusion coefficient decreases
with increasing the delay time. We analytically illustrate this suppression of
diffusion by using stochastic delay differential equations and justify the
feasibility of this suppression by applying the time-delay feedback to a
molecular dynamics model.