Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

Details Heat kernel regularization of the effective action for stochastic reaction-diffusion equations Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

2000-09-27

arxiv.org/abs/cond-mat/0009424v1

Phys.Rev. E63 (2001) 036132

Physics

Condensed Matter

Statistical Mechanics

21 pages, uses ReV-TeX 3.1

Scientific paper

10.1103/PhysRevE.63.036132

The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in $d=0$ and $d=1$, and is one-loop renormalizable in $d=2$ and $d=3$ space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in $d=2$.

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