Field theories and exact stochastic equations for interacting particle systems

Area of Science:

• Statistical Physics
• Chemical Kinetics
• Non-equilibrium Thermodynamics

Background:

• Reaction-diffusion systems are fundamental to many physical and biological processes.
• Understanding the dynamics of interacting particles, including fluctuations, is crucial.
• Existing formalisms like the Doi-Peliti method have limitations in describing certain noise phenomena.

Purpose of the Study:

• To derive a general field theory for the dynamics of interacting particles with reaction and diffusion.
• To relate this field theory to an exact stochastic equation for the density field.
• To clarify the origin of
• imaginary
• Langevin noise in reaction-diffusion processes.

Main Methods:

• Starting from a discrete stochastic jump process.
• Deriving a general field theory for the density field.
• Mapping the derived field theory onto the Doi-Peliti formalism.
• Connecting to large deviation functional techniques for non-equilibrium systems.

Main Results:

• A general field theory describing the dynamics of interacting particles with reaction and diffusion was derived.
• The theory provides an exact stochastic equation for the density field.
• The origin of
• imaginary
• Langevin noise in reaction-diffusion systems was clarified.
• The procedure was shown to be applicable to a wide range of problems.

Conclusions:

• The developed field theory offers a unified framework for studying reaction-diffusion dynamics.
• This work provides a deeper understanding of noise in non-equilibrium systems.
• The methodology is extendable to analyze fluctuations in various non-equilibrium systems within the hydrodynamic limit.