On Nonlinear Diffusion with Multiplicative Noise

TL;DR

This paper investigates nonlinear diffusion with multiplicative noise, revealing a dynamic phase transition and identifying two universality classes with distinct critical behaviors, including anomalies near the upper wall.

Contribution

It introduces a novel analysis of nonlinear diffusion with multiplicative noise, characterizing two universality classes and their critical properties, including anomalous dynamics.

Findings

Identification of two universality classes: upper and lower walls.

Characterization of critical properties for each class.

Discovery of broad power-law distributions in the bound phase.

Abstract

Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall. Two different universality classes, corresponding to the cases of an ``upper'' and a ``lower'' wall, are identified and their critical properties are characterized. While the lower wall problem can be understood by applying the knowledge of linear diffusion with multiplicative noise, the upper wall problem exhibits an anomaly due to nontrivial dynamics in the vicinity of the wall. Broad power-law distribution is obtained throughout the bound phase.