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Numerical Solution of the Mode-Coupling Equations for the Kardar-Parisi-Zhang Equation in One Dimension

Francesca Colaiori·M. A. Moore
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Abstract

We have studied the Kardar-Parisi-Zhang equation in the strong coupling regime in the mode-coupling approximation. We solved numerically in dimension d=1 for the correlation function at wavevector k. At large times t we found the predicted stretched exponential decay consistent with our previous saddle point analysis in [Phys. Rev. E {\bf 63}, 057103 (2001)], but we also observed that the decay to zero occurred in an unexpected oscillatory way. We have compared the results from mode-coupling for the scaling functions with the recent exact results from Praehofer and Spohn [cond-mat/0101200] for d=1 who also find an oscillatory decay to zero.

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Francesca Colaiori, M. A. Moore. 2001-09-24. Numerical Solution of the Mode-Coupling Equations for the Kardar-Parisi-Zhang Equation in One Dimension. https://doi.org/10.1103/physreve.65.017105

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