Glassy Solutions of the Kardar-Parisi-Zhang Equation

Abstract

It is shown that the mode-coupling equations for the strong-coupling limit of the Kardar-Parisi-Zhang equation have a solution for $d>4$ such that the dynamic exponent $z$ is $2$ (with possible logarithmic corrections) and that there is a delta-function term in the height correlation function $〈h(\mathbf{k},\ensuremath{\omega}){h}^{*}(\mathbf{k},\ensuremath{\omega})〉\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(A/{k}^{d+4\ensuremath{-}z})\ensuremath{\delta}(\ensuremath{\omega}/{k}^{z})$ where the amplitude $A$ vanishes as $d\ensuremath{\rightarrow}4$. The delta-function term implies that some features of the growing surface $h(\mathbf{x},t)$ will persist to all times, as in a glassy state.