  We provide geometric conditions on the set of boundary points of infinite
type of a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$ which imply
that the $\bar{\partial}$-Neumann operator is compact. These conditions are
formulated in terms of certain short time flows in suitable complex tangential
directions. It is noteworthy that compactness is \emph{not} established via the
known potential theoretic sufficient conditions. Our results generalize to
$\mathbb{C}^{n}$ the corresponding $\mathbb C^{2}$ results due to the second
author.
