Effective potential for the reaction-diffusion-decay system

TL;DR

This paper applies a formalism to reaction-diffusion-decay systems with noise, deriving a one-loop effective potential that is renormalizable in multiple dimensions and influences system stability and pattern formation.

Contribution

It extends the effective potential formalism to reaction-diffusion-decay systems with noise, demonstrating renormalizability and impact on stability and pattern formation.

Findings

Effective potential is one-loop ultraviolet renormalizable in 1-3 dimensions.

Renormalizability can extend to higher dimensions for specific interactions.

Noise influences the stability and pattern formation in the system.

Abstract

In previous work [cond-mat/9904207,cond-mat/9904215] we have developed a general method for casting stochastic partial differential equations (SPDEs) into a functional integral formalism, and have derived the one-loop effective potential for these systems. In this paper we apply the same formalism to a specific field theory of considerable interest, the reaction-diffusion-decay system. When this field theory is subject to white noise we can calculate the one-loop effective potential (for arbitrary polynomial reaction kinetics) and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions. For specific choices of interaction terms the one-loop renormalizability can be extended to higher dimensions. We also show how to include the effects of fluctuations in the study of pattern formation away from equilibrium, and conclude that noise affects the stability of the system in a way which is calculable.