Diffusive-to-Ballistic transition in a Persistent Random Walk (opens in new tab)

We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim t^{-\alpha}$ and show that the system undergoes a transition at $\alpha=1$, separating a super-diffusive regime for $\alpha<1$ from ballistic regime for $\alpha \geq 1$. Using the results for velocity correlation...