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.
Colaiori
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F
Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, United Kingdom.
Moore
M A
MA