Path-Integral Formulation of Stochastic Processes for the Exclusive Particle Systems

Abstract

We present the systematic formalism to derive the path-integral formulation for the hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and creation operators with the mixed commutation relations, we find the Kramers-Moyal coefficients for the corresponding Fokker-Planck equation (FPE) and the stochastic differential equation (SDE) is derived by connecting these coefficients in the FPE to those in the SDE. Finally, the SDE is mapped onto the field-theory using the path-integral, giving the field-theoretic action which may be analyzed by the renormalization group method. We apply this formalism to the two-species reaction-diffusion system with the drift, finding a universal decay expoent for the long-time behavior of the average concentration of particles in arbitrary dimensions.

2 figures, revtex style. Revised version with minor changes

References in corpus (1)

• Diffusion-limited Reactions of hard-core Particles in one-dimension

Cited by in corpus (9)

• Universality classes in nonequilibrium lattice systems
• Master equations and the theory of stochastic path integrals
• Derivation of continuum stochastic equations for discrete growth models
• Hard core particle exclusion effects in low dimensional non-equilibrium phase transitions
• Two-point correlation functions of the diffusion-limited annihilation in one dimension
• Universality class of the restricted solid-on-solid model with hopping
• Monte Carlo simulations of bosonic reaction-diffusion systems
• Large Scale Simulations of Two-Species Annihilation, A+B->0, with Drift
• Monte Carlo simulations of bosonic reaction-diffusion systems and comparison to Langevin equation description