Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation

We study the mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling regime, focusing on the long time properties. By a saddle point analysis of the mode-coupling equations, we derive exact results for the correlation function in the long-time limit-a limit that is hard to study using simulations. The correlation function at wave vector k in dimension d is found to behave asymptotically at time t as C(k,t) approximately A/k(d+4-2z)(Btk(z))(gamma/z)exp[-(Btk(z))(1/z)], with gamma=(d-1)/2, A a determined constant, and B a scale factor.