Langevin equation with scale-dependent noise

TL;DR

This paper introduces a wavelet-based method for solving the Langevin equation that efficiently handles scale-dependent noise, eliminating the need for renormalization in certain cases, and demonstrates its application to interface growth models.

Contribution

A novel wavelet-based approach for perturbative solutions of the Langevin equation that simplifies handling scale-dependent noise without renormalization.

Findings

Method yields finite results without renormalization for band-limited noise

Applied to Kardar-Parisi-Zhang equation to compute Green function

Demonstrates effectiveness in interface growth modeling

Abstract

A new wavelet based technique for the perturbative solution of the Langevin equation is proposed. It is shown that for the random force acting in a limited band of scales the proposed method directly leads to a finite result with no renormalization required. The one-loop contribution to the Kardar-Parisi-Zhang equation Green function for the interface growth is calculated as an example.