Dynamics of interacting particle systems: stochastic process and field theory

Details Dynamics of interacting particle systems: stochastic process and field theory Dynamics of interacting particle systems: stochastic process and field theory

2007-09-10

arxiv.org/abs/0709.1325v1

J.Stat.Mech.0707:P07024,2007

Physics

Condensed Matter

Statistical Mechanics

Article for the special issue of J Stat Mech on "Dynamics of Non Equilibrium Systems"

Scientific paper

10.1088/1742-5468/2007/07/P07024

We present an approach to the dynamics of interacting particle systems, which allows to derive path integral formulas from purely stochastic considerations. We show that the resulting field theory is a dual version of the standard theory of Doi and Peliti. This clarify both the origin of the Cole-Hopf map between the two approaches and the occurence of imaginary noises in effective Langevin equations for reaction-diffusion systems. The advantage of our approach is that it focuses directly on the density field. We show some applications, in particular on the Zero Range Process, hydrodynamic limits and large deviation functional.

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