Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation
Abstract
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 which is hard to study using simulations. The correlation function at wavevector k in dimension d is found to behave asymptotically at time t as C(k,t) 1/kd+4-2z (Btkz)γ/z e-(Btkz)1/z, with γ=(d-1)/2, A a determined constant and B a scale factor.
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