Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-08-14
Phys. Rev. E 62, 7642 (2000)
Physics
Condensed Matter
Statistical Mechanics
2 figures, revtex style. Revised version with minor changes
Scientific paper
10.1103/PhysRevE.62.7642
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.
Kim Doochul
Park Jeong-Man
Park Su-Chan
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