Year: 1996
Type: article
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 theorem. 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 theory 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 perturbation 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 1. Surprisingly, however, their effect on the correlation function is substantially smaller.
Authors: Erwin Frey, Uwe Claus Täuber, Terence Hwa
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2020243869