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 (12)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Langevin Equation for the Density of a System of Interacting Langevin Processes
• Macroscopic fluctuation theory for stationary non equilibrium states
• Fluctuations in Stationary non Equilibrium States
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Macroscopic current fluctuations in stochastic lattice gases
• Integration of Langevin Equations with Multiplicative Noise and Viability of Field Theories for Absorbing Phase Transitions
• `Real' vs `Imaginary' Noise in Diffusion-Limited Reactions
• Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry
• Nonequilibrium Dynamics in Low Dimensional Systems
• Pair Contact Process with Diffusion: Failure of Master Equation Field Theory
• Some puzzling problems in nonequilibrium field theories

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