Monte Carlo simulations of bosonic reaction-diffusion systems

TL;DR

This paper introduces an efficient Monte Carlo simulation method for bosonic reaction-diffusion systems, validating it through models like the annihilation process and PCPD, and compares results with renormalization group predictions.

Contribution

The paper presents a novel Monte Carlo simulation approach tailored for bosonic reaction-diffusion systems, enabling accurate analysis and comparison with theoretical RG results.

Findings

Numerical data align with RG predictions for the annihilation model.

Bosonic PCPD exhibits the same critical behavior as the standard PCPD.

The bosonic model maintains invariance under Galilean transformation.

Abstract

An efficient Monte Carlo simulation method for bosonic reaction-diffusion systems which are mainly used in the renormalization group (RG) study is proposed. Using this method, one dimensional bosonic single species annihilation model is studied and, in turn, the results are compared with RG calculations. The numerical data are consistent with RG predictions. As a second application, a bosonic variant of the pair contact process with diffusion (PCPD) is simulated and shown to share the critical behavior with the PCPD. The invariance under the Galilean transformation of this boson model is also checked and discussion about the invariance in conjunction with other models are in order.