Aging in Models of Non-linear Diffusion

TL;DR

This paper analyzes non-linear diffusion models, deriving exact two-time correlation functions that reveal normal, anomalous, and aging behaviors, and discusses fluctuation-dissipation theorem violations linked to non-conservation of mass.

Contribution

It provides an exact calculation of correlation functions in non-linear diffusion models and explores the origins of aging and FDT violations in these systems.

Findings

Correlation functions depend on time differences and exhibit aging.

Models show both normal and anomalous diffusion behaviors.

Aging may result from non-conservation of total mass.

Abstract

We show that for a family of problems described by non-linear diffusion equations an exact calculation of the two time correlation function gives C(t,t')=f(t-t')g(t'), t>t', exhibiting normal and anomalous diffusions, as well as aging effects, depending on the degree of non-linearity. We discuss also the form in which FDT is violated in this class of systems. Finally we argue that in this type of models aging may be consequence of the non conservation of the "total mass".