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

Francesca Colaiori·M. A. Moore
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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)\simeq 1/k^{d+4-2z} (Btk^z)^{γ/z} e^{-(Btk^z)^{1/z}}, with γ=(d-1)/2, A a determined constant and B a scale factor.

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Francesca Colaiori, M. A. Moore. 2000-11-10. Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation. https://doi.org/10.1103/physreve.63.057103

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