Field theoretic approach to metastability in the contact process

TL;DR

This paper develops a quantum field theoretic framework to analyze metastability in the contact process, providing perturbative corrections to mean-field results and validating them against numerical simulations.

Contribution

Introduces a quantum field theoretic approach to the contact process, deriving corrections to mean-field predictions for metastability and stationary states.

Findings

Perturbative corrections improve mean-field predictions.

Results agree well with numerical simulations.

Provides insights into both typical and rare fluctuation properties.

Abstract

A quantum field theoretic formulation of the dynamics of the Contact Process on a regular graph of degree z is introduced. A perturbative calculation in powers of 1/z of the effective potential for the density of particles phi(t) and an instantonic field psi(t) emerging from the quantum formalism is performed. Corrections to the mean-field distribution of densities of particles in the out-of-equilibrium stationary state are derived in powers of 1/z. Results for typical (e.g. average density) and rare fluctuation (e.g. lifetime of the metastable state) properties are in very good agreement with numerical simulations carried out on D-dimensional hypercubic (z=2D) and Cayley lattices.