Field theories and exact stochastic equations for interacting particle systems

Abstract

We present a new approach to the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further the issue of the 'imaginary' Langevin noise that appears in the context of reaction/diffusion processes. Our procedure applies to a wide class of problems and is related to large deviation functional techniques developed recently to describe fluctuations of non-equilibrium systems in the hydrodynamic limit.

4 pages, no figures

References in corpus (2)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Some puzzling problems in nonequilibrium field theories

Cited by in corpus (4)

• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• On the Brownian gas: a field theory with a Poissonian ground state
• Dynamics of interacting Brownian particles: a diagrammatic formulation
• Macroscopic Expression Connecting the Rate of Energy Dissipation and Violation of the Fluctuation-Response Relation