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 $d>\mathrm{}4\mathrm{}$ 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 $〈h(\mathbf{k},\omega )h^{*}(\mathbf{k},\omega )〉=\left(A/k^{d+4-z}\right)\delta \left(\omega /k^z\right)$ where the amplitude $A$ vanishes as $d\to 4$. 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.