Glassy Solutions of the Kardar-Parisi-Zhang Equation

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 $〈h(k,{ω}){h}*(k,{ω})〉{{0ex}{0ex}}={{0ex}{0ex}}(A/{k}^{d+4{-}z}){δ}({ω}/{k}ᶻ)$ where the amplitude $A$ vanishes as $d{→}4$. The delta-function term implies that some features of the growing surface $h(x,t)$ will persist to all times, as in a glassy state.