# Mode coupling and renormalization group results

# for the noisy Burgers equation

Erwin Frcy, U.C. Tauber and T. Hwa

## Abstract

We investigate the noisy Burgers equation (Kardar--Parisi--Zhang
equation in 1+1 dimensions) using the dynamical renormalization
group (to two--loop order) and mode--coupling techniques. The
roughness and dynamic exponent are fixed by Galilean invariance
and a fluctuation--dissipation the- orem. The fact that there
are no singular two--loop contributions to the two--point vertex
functions supports the mode--coupling approach, which can be understood
as a self--consistent one--loop the- ory where vertex corrections
are neglected. Therefore, the numerical solution of the mode coupling
equations yields very accurate results for the scaling functions.
In addition, finite--size effects can be studied. Furthermore,
the results from exact Ward identities, as well as from second--order
per- turbation theory permit the quantitative evaluation of the
vertex corrections, and thus provide a quantitative test for the
mode--coupling approach. It is found that the vertex corrections
themselves are of the order one. Surprisingly, however, their
effect on the correlation function is substantially smaller.

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