Drift-diffusion decay time (source code)

= Drift-diffusion decay time
{title2=$t_*\sim D/v^2$}

For constant <diffusion coefficient> $D$ and <drift velocity> $v\ne0$, the balance $|v|t\sim\sqrt{Dt}$ gives the characteristic <length> $D/|v|$ and <time> $D/v^2$. The fundamental <Gaussian distribution> of the <advection-diffusion equation> has a fixed-position exponential factor $\exp[-v^2t/(4D)]$. Total <probability> is still conserved: this describes <probability> moving away from a fixed observation region, rather than disappearance of the <particle>. At zero drift, this finite exponential <time> scale is absent.