Lognormal-like statistics of a stochastic squeeze process Academic Article uri icon

abstract

  • We analyze the full statistics of a stochastic squeeze process. The model's two parameters are the bare stretching rate $w$ and the angular diffusion coefficient $D$. We carry out an exact analysis to determine the drift and the diffusion coefficient of $log(r)$, where $r$ is the radial coordinate. The results go beyond the heuristic lognormal description that is implied by the central limit theorem. Contrary to the common ``quantum Zeno'' approximation, the radial diffusion is not simply ${D}_{r}=(1/8){w}^{2}/D$ but has a nonmonotonic dependence on $w/D$. Furthermore, the calculation of the radial moments is dominated by the far non-Gaussian tails of the $log(r)$ distribution.

publication date

  • January 1, 2017