The ideas behind the Self Consistent Expansion

TL;DR

The paper explains the Self Consistent Expansion (SCE), a method for analyzing strongly coupled non-equilibrium systems like KPZ, which are difficult to study with traditional perturbative techniques.

Contribution

It provides a clear and accessible presentation of the SCE method, highlighting its ability to handle strong coupling regimes in non-linear stochastic field theories.

Findings

SCE generates a self-adjusting small parameter.

It offers a regular expansion structure for complex systems.

The method is applicable to KPZ and similar models.

Abstract

In recent years we have witnessed a growing interest in various non-equilibrium systems described in terms of stochastic non-linear field theories. In some of those systems like the KPZ and related models, the interesting behavior is in the strong coupling regime, which is inaccessible by traditional perturbative treatments such as dynamical renormalization group (DRG). A useful tool in the study of such system is the Self Consistent Expansion (SCE), which might be said to generate its own "small parameter" .The self consistent expansion (SCE) has the advantage that its structure is just that of a regular expansion, the only difference is that the simple system around which the expansion is performed is adjustable. The purpose of the this article is to present the method in a simple and understandable way, that hopefully will make it accessible to a wider public working on non-equilibrium statistical physics.