Real Space Renormalization Group for Langevin Dynamics in Absence of Translational Invariance

TL;DR

This paper introduces an exact real space renormalization group method for Langevin dynamics, demonstrating algebraic temporal behavior of Green functions on complex structures like fractals, with implications for interface growth.

Contribution

It presents a novel, exact dynamical renormalization group approach for Langevin equations on arbitrary structures, including fractals, revealing new fixed points and dynamical behaviors.

Findings

Algebraic temporal law for Green functions on arbitrary structures

Identification of two distinct fixed points on fractals

Connection to interface growth dynamics

Abstract

A novel exact dynamical real space renormalization group for a Langevin equation derivable from a Euclidean Gaussian action is presented. It is demonstrated rigorously that an algebraic temporal law holds for the Green function on arbitrary structures of infinite extent. In the case of fractals it is shown on specific examples that two different fixed points are found at variance with periodic structures. Connection with growth dynamics of interfaces is also discussed.