Monte Carlo simulations of bosonic reaction-diffusion systems and comparison to Langevin equation description

TL;DR

This paper uses Monte Carlo simulations to study one-dimensional bosonic reaction-diffusion systems and compares the results with Langevin equation descriptions, confirming their equivalence and exploring critical behaviors.

Contribution

It demonstrates the numerical equivalence between master equations and Langevin equations for bosonic models and investigates critical phenomena in coupled bosonic systems.

Findings

Confirmed the equivalence of master and Langevin equations for the annihilation model.

Derived Langevin equations for the pair contact process with diffusion.

Numerically validated the asymptotic correlation functions for the models.

Abstract

Using the Monte Carlo simulation method for bosonic reaction-diffusion systems introduced recently [S.-C. Park, Phys. Rev. E {\bf 72}, 036111 (2005)], one dimensional bosonic models are studied and compared to the corresponding Langevin equations derived from the coherent state path integral formalism. For the single species annihilation model, the exact asymptotic form of the correlation functions is conjectured and the full equivalence of the (discrete variable) master equation and the (continuous variable) Langevin equation is confirmed numerically. We also investigate the cyclically coupled model of bosons which is related to the pair contact process with diffusion (PCPD). From the path integral formalism, Langevin equations which are expected to describe the critical behavior of the PCPD are derived and compared to the Monte Carlo simulations of the discrete model.